"Pay a price based on spell level"

Note: I use the term "Pay" repeatedly. In this post this simply means to deduct from their starting cash according the published Wealth By Level (WBL) chart.

The chart at the bottom of this answer is the base amount of spells a wizard gets for free. The only answers for "how many additional spells a wizard has learned at upper levels" I've found so far are to charge 150 gp for each spell. Supposedly this is to cover the 100 gp price of the page plus the sell price of the spell in a wizard's spellbook.

This is flawed on its face since it costs 100 gp per page, but each spell takes 1 page per level of the book. So a level 2 spell would cost 200 gp to add to a book. Using the intended logic this would cost 250 gp. So this is the only answer I could come up with.

However, the biggest drawback to this system is that by upper levels the WBL table has them starting with so much coin they could effectively have nearly any spell. (level 15 starts with 200,000 GP) They would have to have additional spellbooks to hold over the 100 page limit but big deal at this point.

The other drawback is that it is ridiculous to assume that anyone has killed this many wizards or convinced that many wizards to share their books. The rulebooks make this sound like a rarity due to how wizards safeguard their research..and the normal charge is 50 gp × spell level (+the cost of writting the spell into their own spellbook). A way around this is to have them pay full price for scrolls. While this solves the "found too many wizard books" problem, it may make the price go too far in the other direction.

Ways to overcome the drawbacks:

1. Set an arbitrary number of how many additional spells they could have. I don't like this b/c how do you fairly pick an arbitrary number?
   
2. Set a limit of how many spells they get at the "found spellspook" price (100gp per spell level +50gp) and then allow them to get how many ever scrolls they want. (100gp per spell level + retail price of scroll)
   
   • This still has the problem of how to pick a fair arbitrary number?
     
3. Give them a set amount they can use on learning new spells. Still an arbitrary number, but atleast one that is more feasible. ie, you can set a max of 30% of wealth be spent on a single item, so the same principal or even cap could be set on learning spells.

Base Wizard Spells per Level

1. 3+Int
2. +2 (1st lvl)
3. +2 (any combo of 1st or 2nd lvl)
4. +2 (any combo of 1st or 2nd lvl)
5. +2 (any combo of 1st 2nd or 3rd lvl)
6. +2 (any combo of 1st 2nd or 3rd lvl)
7. +2 (any combo of 1st 2nd 3rd or 4th lvl)
8. +2 (any combo of 1st 2nd 3rd or 4th lvl)
9. +2 (any combo of 1st 2nd 3rd 4th or 5th lvl)
10. +2 (any combo of 1st 2nd 3rd 4th or 5th lvl)
11. +2 (any combo of 1st 2nd 3rd 4th 5th or 6th lvl)
12. +2 (any combo of 1st 2nd 3rd 4th 5th or 6th lvl)
13. +2 (any combo of 1st 2nd 3rd 4th 5th 6th or 7th lvl)
14. +2 (any combo of 1st 2nd 3rd 4th 5th 6th or 7th lvl)
15. +2 (any combo of 1st 2nd 3rd 4th 5th 6th 7th or 8th lvl)
16. +2 (any combo of 1st 2nd 3rd 4th 5th 6th 7th or 8th lvl)

Let's review the basic numbers first, before we get into how Wizards break them: at level 1, every character picks 2 at-wills, 1 encounter power, and 1 daily. At level 2, they pick up a utility power too.

At-will powers

So, you have to choose two at-wills, right?

But there's something else first. Some classes have feature powers, and the Wizard's are their four cantrips. You get these automatically. You already have four at-wills, just by being a Wizard.

These do not count toward the 2 you pick. So pick two more Wizard Attack 1 at-wills.

Notice that the Cantrips have no level mentioned. Neither do Racial powers. This is your hint that it's an automatic feature that you get in addition to however many at-wills/encounters/dailies/utilities you get at your level. (The Paladin also has four class feature powers, but two of those are encounter powers.)

Total level 1 at-wills: 6. And then some racial features might give you more.

Encounter powers

1 at first level. Gain encounter powers the same as any other class.

A lot of races also give you an encounter power, but like I mentioned about the at-wills: this comes in addition to whatever single encounter power you pick, and doesn't count toward your limit of 1.

The Spellbook: Dailies and Utilities

This is where Wizards have some novelty, and where they get a bit complicated.

Every class has a notion that they have X powers and they have them available every day. Wizards break this mold and do things very differently.

When the Wizard might learn a daily or utility power — including their first-level daily and second-level utility — instead, the Wizard picks two dailies, or two utilities. They write these two down in their spellbook. Then as the feature says...

After an extended rest, you can prepare a number of daily and utility spells according to what you can cast per day for your level. You can’t prepare the same spell twice.

You pick a bunch, and these are your daily and utility powers for the day. So you know twice as many daily powers and twice as many utility powers as any other class. But at the beginning of your adventuring day, you pick the same amount as anyone else, and those are your dailies and utilities for the day.

So at level 2, instead of the usual 1 daily and 1 utility, you'll have twice that many - 2 dailies and 2 utility powers - written in your spellbook. But after you rest, you'll pick 1 of those dailies and 1 of those utility powers, and you'll have those available to use for the day. So on any given day, you still have access to the same amount of daily and utility powers as any other character - but uniquely, Wizards can change the powers they have access to day-to-day between those in their spellbook.

At a level where you might be alotted 3 daily powers, you'll have 6 in your spellbook, and pick any 3 of those 6 at the beginning of an adventuring day. Etc.

Rituals

You also get to start with some rituals written in your spellbook. This is separate to your powers entirely, and a different casting system every player character shares. You just get to start off knowing some rituals, where others will have to find them or buy them.