[RangerWickett]

He could get magic missile and fireball, and take a metamagic feat or two, and have a ton of mook-killing power. Or he might go for, say, minor image and teleport. Either is better than the current version and, I feel, better than your system which would let a 19th level fighter pick up dozens of spells by investing just one level in wizard.

Maybe make spells known a function of your total caster level, and have a universal spell list. If your caster level goes up due to a nonspellcasting class's level, you have to pick spells from the universal list.

What if your caster level increases when you haven't yet taken any spellcasting classes yet, though? Hm. Maybe you don't select any spells, and whenever you take a spellcasting class, you have to fill in all the backlog with spells from your current class. Iffy.