My solution for years has been "powers instead of items," so I'll go into a bit of detail on how I fix some of the minor roadbumps that occur with that problem.
Temporary magic items (scrolls, wands...) are a problem, since it becomes unclear what the character's "wealth" (for magical equipment equivalent powers) is.
Not as much as you might think. First of all, scrolls, wands (bundles of 50 scrolls) and the like aren't often the most grevieous offenders of this category, and so can usually be allowed as they are, without any need to turn them into powers. Disposable magic items aren't really a part of your equipment, per se, because they'll be discareded eventually. A bundle of scrolls, a wand, a potion, a staff...IMC, I let them in virtually unchanged because the are temporary, so the aren't meant to be a permenant part of your character's power.
You can also still make them non-items if you wish, Things like "wearing spells" so that they're already cast, and just have their effects latent can be used. Or you can secret them into things -- when the party sorcerer expends his last
fireball, inform him that he still thinks he can cast it a few more times; keep track of the charges on these items youself. The ExPsiHB even uses tatoos as an analouge to potions, so the idea is out there...
It also stretches disbelief to have powerful or blunt magical effects. I found the best method to deal with it is to have the characters be divine scions awakening into their powers - as this also solves the "what IS XP anyways, and how come I can increase in power so rapidly?" problem. The option of bonding/tattooing rituals and so on would also be cool. But for me just letting the character fly 1/day without some supernatural explanation doesn't work.
I've always tied it into the charater's own history and motives, thinking of them more like highly specialized class abilities. It's the warrior who always fancied himself an astronomer who gets to fly to take him closer to the stars, or the barbarian whose jumps almost defy gravity, or the sorcerer who has specialized in air magic...it's not just any character, it reflects the character's powers. That belt of giant's strength is probably going to the party's warrior anyway, saying that the party's warrior has developed a supernatural strength from having
bull's strength cast on him so many times seems to make perfect sense.
Material magical items, such as a magical axe or so on, are also a problem to properly represent with this model. I generally allow both, as it's just cool for the wizard to have his staff or so on.
I'm not sure what you mean by "material" magic items...but yeah, it is cool to allow those disposable or iconic magic items, and there's no reason those have to be taken out.
You need to decide whether to demand double price (as the items don't take up slots) or not.
My rules say no, because even though it doesn't take up a slot, they also can't sell it, can't exchange it, can't give it to someone who might benefit more, can't bribe the enemy with it, can't dip it in acid to test it, and generally have a few more limitations (ESPECIALLY includign the "you can't sell it" part, which puts a damper on their treasure and means that upgrading that +2 Str to a +4 is much more difficult) that an actual item that didn't take up slots would.
Finally, in such a campaign expensive nonmagical gear can augment the characters further; such equipment must be somehow balanced wtih the characters as well (this is more of a problem at low levels).
Not so much. That +2 to Strength works just like a belt in that it's an enhacement bonus, and it is magical. It can be dispelled, and it doesn't stack with most magic. You can't go out and buy a belt to augment your magically discovered strength further.