Large Level Gaps Are Bad

Here's the problem. You have a level 9 party. They're probably fighting stuff somewhere around their power level. If you throw a level 1 character into that, they are both highly ineffective (anything with a save will be made, few spells, limited ability to contribute), and absurdly fragile (very low HP, lower saves, probably limited money for gear unless you give them level 9 equivalent treasure).

That combination just doesn't work in 3.5. An experienced player can maybe make it work by knowing all the tricks to get the most out of their tiny allotment of level 1 spells. A newbie will not, and one mistake will get them killed. They do not have a margin for error, and as a new player they need a margin for error more than anyone else.

As the DM, you'd have to avoid trying to kill that character. You can't even do things like throw fireballs around with your NPCs, because a single one anywhere near that character and it's dead.

You could tone things down instead, but then the level 9 characters will steamroll over everything and not be challenged. That's also bad.

Given that, your best bet is to start the new character at level 9.

Mentorship

You and the other players will have to help mentor your new player. That goes with a level 1 character, and it goes with a level 9 character. The main difference is that the level 9 character is going to have more abilities, and some margin for error (a single melee attack won't kill a level 9 character very often).

Your new player will need help building a character, picking gear, learning what their stats mean, when to use skills, and so on. You and the other players can help with that in the first couple of sessions, mostly by helping with character creation, answering questions, encouraging questions, and offering hints and suggestions.

Gradual Spellbook Additions

Since your new player wants to play a spellcaster, the real overwhelming thing is trying to master the spell system and the large spell list. That's where you can help.

Shrink the list. A lot. Start the player off with a pared down spell list, where you pick out a handful of essential spells. If the player wants to, let them look through the book and pick out a few more that sound interesting. Don't give them 100 spells to start. Use a much smaller number (under 30).

As the player starts to grasp things in future sessions, start adding spells. For a Wizard this is easy, as you can say what's in the spellbook initially, and you can introduce spells to add to it later. For a Divine Caster, you may just have to explain why you want him to focus on a smaller set of spells initially to get the hang of it, and that the other ones are available if he wants to use them in the future.

I know when a friend of mine played a caster for the first time (a Cleric, which is a great class), we sat down together and built a "typical daily memorization list". Those were the spells he'd prepare each day, normally. He could make additions or changes if events warranted it, but I built the first list with him and he didn't have to try to figure out what spells were must have on his own. It made trying to figure out what to cast at first a lot easier for him, because that list is much shorter.

For a spontaneous caster, you can handle it differently depending on the class. Something with a fixed list like Beguiler you can treat like a Divine Caster: shorten the available list up a bit initially, and then add spells back as the player starts to get the hang of it. For Sorcerer where you have to pick the spells you will use forever... well, I'd pick an initial list of spells, and then give the new player the option to swap them out later if he decides he wants something else. Sorcerers already have this option every even numbered level, but he will have missed some chances to do it by starting at level 9 and by not knowing what to pick initially. You can be a bit more flexible with the swapping rules by allowing one time swapping of any spell that he came into the game with, so he can customize his character once he understands how it works.

So Which Spellcaster Should He Be?

You mentioned spells, but not which class he's going to play. If he's already picked a class to play, great! If he hasn't picked a class yet, I have a couple of recommendations.

1. Beguiler - Spontaneous caster, so no preparation of spells at the start of the day is required. Preparation can often be a real stumbling block for new players, so this takes it out of the way. The fixed spell list is a bit limiting, but he won't have to choose which spells he knows, as he just gets all of the ones the class has access to. Also gets d6 HD and access to light armor, which makes them tougher than the Sorcerer (handy for a new player). A lot of skill points and a good skill list is handy too. This is a pretty solid "pick up and play" spellcaster that doesn't need much book keeping.
2. Cleric - Has to prepare spells, which may be an issue. But other than that, there's a lot to recommend here. It's easy to make a Cleric that's tough as nails (full plate, two good saves, and d8 HD go a long way!), their spell list is strong, they can be strong melee combatants, easy access to healing whenever you want it, and there's no spell book to manage.

Druid and Wizard are both great classes, but they're also harder to play and may not be an ideal choice for a new player. That's not to say he can't play them, because he can. He'll just need more help:

• Druids have to also manage an animal companion, and wild shape. The animal companion can be a plus, because at level 9 you can get something that's pretty tough (like a Brown Bear or Dire Wolf), but now there's more stats to know and more things to manage. Wild Shape exacerbates that problem even more by changing the player's stats themselves.
• Wizards not only have to prepare spells each day, but also have to keep track of which ones they're allowed to prepare due to what's in their spellbook. They're also very, very fragile if you don't know how to mitigate that, and the familiar is an extra thing to manage if you don't trade it out for something else.

My Rule of Thumb

There isn't an official rule of thumb. Mine (and it seems to be pretty common amongst players I know) is that the party should be the same level unless there is a good reason why they're not (someone spending XP on item creation feats for example). If a new player joins, I put him at the same XP as everyone else, and try to keep treasure from being too different (though the new person may start with a bit less, as I typically give new players standard wealth from the DMG).

Level is one of those things that can make someone horribly ineffective if you set them back too far. They can make that up by being more optimized than everyone else is, or know how to use their abilities more successfully, but the game in my experience just works better when party members don't have level gaps between them.

A small gap is one thing, but a level 1 new player in a level 9 party is just unworkable.

Original Answer: Lots of Guesswork

I don't think any currently-published materials address the effect of magic items on encounter difficulty, but the rules assume a certain volume of magic items-per-level, and the difficulty calculations and monster challenge ratings probably take that into account. However, if your PCs are exceeding the daily recommended allowance of magic items (very vaguely defined, but see addendum below), XP thresholds based on their true experience levels are almost certainly useless.

That being said, it's possible to compare the powers of magic items to the bonuses players get by gaining experience levels. A weapon that confers +1 to attack and damage rolls is functionally the same, in-combat, as gaining 2 points in the relevant ability score. An item that lets you cast a certain spell once per day is "the same as" gaining a spell slot.

Combat-oriented magic items denoted by the DMG as uncommon or rare have effects that amount to a fraction of the increase in power received by gaining a single level, at least in the low-level tier for which they're recommended (per DMG 135). At level 4, the Druid gets an ability score improvement (combat-equivalent to that +1 weapon), another 2nd-level spell slot (roughly combat-equivalent to that spellcasting item), some more hit points, and another hit die. So if you give both those items to a level 4 Druid, that PC is almost level 4, for combat purposes. You might want to calculate two different XP thresholds, treating the PC as level 3 and then as level 4, or you might want to split the difference between them.

This approach can't account for the versatility that magic items provide. To a Wizard who already can cast scorching ray, a circlet of blasting is a fairly disappointing reward, but to a hammer-oriented Champion Fighter it opens up a world of hands-free blasting possibilities.

Combat-oriented items denoted by the DMG as very rare or rarer provide bonuses that far outstrip the benefits of ascending from experience level 3 to experience level 4, and may even be equivalent to a full experience level or more for PCs at level 15 or above. I have no experience with high-level 5e and can't really speak to that. It's not hard to guess, though, that if you provide your players with a lot of very rare-rated magic items, your hopes of accurately calculating combat difficulty will fly out the window.

Addendum: Lots of Rolling on Tables

On close inspection, the DMG is actually fairly specific about how many magic items a party should get. It just happens to establish this in an extremely roundabout way. On page 133: "Over the course of a typical campaign, a party finds treasure hoards amounting to seven rolls on the Challenge 0-4 table, eighteen rolls on the Challenge 5-10 table, twelve rolls on the Challenge 11-16 table, and eight rolls on the Challenge 17+ table."

Rather than reproducing the Challenge 0-4 table and the many tables it references, I'll present here only a few relevant values. A treasure horde generated for CR 0-4 has:

• 36% chance of no magic items.
• 24% chance of 1d6 items from Magic Item Table A.
• 15% chance of 1d4 items from Magic Item Table B.
• 10% chance of 1d4 items from Magic Item Table C.
• 12% chance of 1d4 items from Magic Item Table F.
• 3% chance of 1 item from Magic Item Table G.

Now, Table G is a level 4 adventurer's dream. You have a 10% chance to get a +2 weapon, which is categorically overpowered for this tier. If that's not broken enough, you might end up with a mace of disruption or a wand of wonder. A 3% chance of rolling on this table at this tier seems like a bit much to me, but I'm no wizard of a coast.

This is what the guidelines tell us, though, so let's pretend to roll 7 times on the Challenge 0-4 table. If we apply my liberal arts degree's understanding of the law of averages, I predict we'll end up getting no magic items twice, roll a total of 2d6 times on Magic Item Table A, and roll 1d4 times each on tables B, C, and F.

Table A is 98% consumables and a couple of fairly mundane utility items. Rolling 7 times, we'd probably get 3 or 4 potions of healing, 3 or 4 low-level spell scrolls (hopefully from the spell list of a caster in your party!), and maybe—if you're really lucky—a driftglobe.

Table B is 64% consumables, a few somewhat more interesting utility items, and a very few items like mithral armor with fairly remote combat applications. We'll probably get a couple of fun potions, but let's say we picked up that mithral armor. I won't tell if you don't.

Rolling twice on Magic Item Table C, we might pick up a necklace of fireballs, but far more likely we'll get a couple rare-ish potions.

On Magic Item Table F, we're looking at stuff like a +1 weapon, a circlet of blasting, or some gauntlets of ogre power. That is, a couple of those "combat-equivalent to gaining part of a level" items described above.

By the end of the level 1-4 tier, we've amassed (and likely consumed) quite a few potions and scrolls. Their effect on combat isn't nothing, but it's not really enough to impact any combat difficulty calculations.

Despite several opportunities to pick up some overpowered weapons or equipment, our permanent acquisitions are probably limited to two or three rare-grade items. And these we have to split among the whole party! Only a very greedy and very lucky PC will be carrying enough magic items to be treated as one experience level higher for combat purposes. It might not be a bad idea, though, to calculate your XP thresholds as if one PC is one level higher, if the efficacy of one additional experience level is spread out across the entire party.

I will spare you my "calculations" for your campaign's treasure horde yields in the level 5-10 tier and above, but I notice those tables continue to draw a lot from magic item tables A, B, and C. Following the guidelines on page 133, PCs can't really rely on these treasure hordes to contain permanent magic items until the level 17+ tier. Suddenly the limit on attunement to a maximum of three items doesn't seem like a huge deal!

Of course, relying exclusively on these tables is going to make for one boring campaign. So many potions of giant strength! Magic items are used best as storytelling props, hand-picked for their roles in the scenarios you create. But the printed guidelines clearly intend for a given PC to pick up only a small collection of permanent magic items over his or her career. I can conclude with some confidence that the intended magic item distribution is so sparse as should not affect encounter difficulty calculations.

But that conclusion answers a different question! For present purposes, the upshot to this excess of analysis is that we now have a benchmark for what the 5e rules consider the correct number of magic items ("not very many"), and can gauge by our distance from that figure how overpowered our party is for purposes of encounter difficulty calculation.

Glib Extra Answer

If your PCs have so many magic items that the monsters you pit against them are no longer a challenge, try giving some magic items to the monsters.