XP Penalty
You can remove the multiclass XP penalty by playing a race with one of those as your favored class (like Elf), or as Human, where your class with the most levels just doesn't count no matter what it is. Human is pretty much always a good choice anyway.
And that's if your DM actually uses those rules. In my experience, quite a lot don't enforce those XP penalty rules.
Class Choice - Look at Beguiler
Sorcerer would work as a first class choice. Beguiler (Players Handbook II) would work even better, as it's also a spontaneous caster, only one whose key stat is Intelligence (same as the Wizard). This plays off a stat you already need and fits the idea of a "learned" character who also has innate ability.
Add Ultimate Magus as a Prestige Class
If you go Beguiler/Wizard or Sorceror/Wizard, you can then go into the Ultimate Magus (Complete Mage) prestige class, and boost spellcasting from both at the same time. One would go up faster than the other, but the class also lets you use spells from one to power metamagic from the other, and it can do some pretty neat things. See also What exactly are Prestige classes, and what purpose do they serve?
Instead of just taking the spontaneous spells as a one off thing, this lets you develop both of them as the character learns to blend his two types of magic together. It's a pretty neat (and powerful) concept.
This answer has some useful information on how to get the most out of Ultimate Magus.
Spontaneous Divination
Wizards can get the ability to cast any Divination spell spontaneously by trading their 5th level bonus feat for this ACF. It does what it says - you can trade any prepared spell you have to spontaneously cast any Divination spell you can cast of equal or lower level.
Other Option - Reserve Feats
If you don't want to multiclass but still want some spontaneous abilities, reserve feats are another option. These let you use some power so long as you have a spell "in reserve" that you don't cast. Examples are things like being able to do small flame strikes, shoot lightning, summon elementals, create force darts, or do some minor magic disruption. You can get that as early as level 3, and you can use them infinitely so long as you don't cast the reserved spell.
It's not as versatile as true spontaneous casting, but it also doesn't require multiclassing at all. So I felt it was wroth mentioning.
There aren't many things that fit your criteria--either a low-level spell that creates a comfy thing to sleep on or a magic item that makes a comfy thing to sleep on that's appropriate for a level 4 character. Nonetheless, here's
One Spell and Two Items
- The 2nd-level Sor/Wiz spell Leomund's tiny igloo [conj] (Fr 101) for 2 hours/level creates an igloo for Medium you and 3 Medium friends. Its walls have hardness 0 and 3 hp per caster level, it withstands up to (but not including) hurricane winds, and its magically heated. It's very cool.1
- The slotless item survival pouch (MIC 187-8) (3,300 gp; 5 lbs.) grants the possessor the ability as a standard action 5/day to pull from it a variety of things, including a tent and 2 bedrolls as but 1 of its 5 uses per day. Other items include a lit campfire and a summoned-like decked-out mule (although it won't fight for you).
- The slotless item Heward's fortifying bedroll (CM 132-3) (3,000 gp; 2 lbs.) grants the user the ability to get 8 hours rest in just 1 hour.
Both items are expensive for a lone level 4 character, but splitting the cost among party members makes either more palatable. The pouch is extremely versatile, and if your party's permanently camping it should provide everything your party needs in a 5 lb. package. And while it's a little gross taking shifts sleeping in the same fortifying bedroll, it's only an hour--just use the spell prestidigitation afterward to clean off leftover barbarian lice.2 The advantage of shorter watches with more people on them is huge.
- Sorry.
- The lice are from the barbarian not actual barbarians.
Best Answer
Yes and no
This is what the ability gains every four levels represent: actions your character is taking to improve an ability score. Most players don’t spend a lot of time discussing why they get those gains (since it’s “obvious” why the barbarian gains more Strength or the cleric gains more Wisdom), but the function of this mechanic is precisely to model the kinds of training that you are discussing.
In general, the game leaves the description of downtime training, maintenance, and so on very vaguely defined; that is supposed to be up to the players to describe. But leveling up isn’t magic. It’s an abstraction for exactly that kind of training and practice. You are assumed to be constantly studying, or lifting, or practicing skills, or maintaining gear, and so on, during any downtime you have. It’s all abstracted away, and then at some point it “all comes together” for you, you have that eureka moment, and you level up.
(No, this system does not bear close scrutiny.)
This is an extremely slow way to gain any ability score, however, and the game’s math has it “already accounted for,” so using it to increase Strength as a wizard is, from the game’s perspective, basically the same as losing Intelligence – since the game assumes that’s where you’ll be putting it (and monster designers take the resulting save DC increase into consideration when deciding monsters’ saving throw bonuses). But you still can.
Ultimately, wizards have exceedingly little use for Strength. A handy haversack and portable hole are great items anyway, so carrying gear isn’t all that important, touch attacks are trivial in most cases anyway (and you usually prefer ranged ones, which use Dexterity). The only real problem is the risk of being rendered unable to move by Strength drain or damage.