For an upcoming game, I want to try the idea of a low-magic-item Golarian. There will be no magic weapons, armor, wondrous items, etc. The only crafted magic items I will be keeping in the game are consumable magic items. - wands, scrolls, potions, etc., and even then in limited supply.
Are there any alternative power-gain systems people have tried out? I don't want a party that is completely reliant on items to increase in power. Thanks in advance!
There are threads on the issue, but no one method has gain favor over the others. The homebrew section is probably a good place to look.
Short version? You don't.
D&D and, by extension, Pathfinder is a phenomenally high-magic game. If you want a higher-magic game, you're getting into the realm of Exalted (and even that's easier to adapt to low-magic). Even at level three, you're beginning to feel the hole, hard. Magic items are a hard-wired assumption around which the game revolves. If you want a robust low-magic game, play in a different system. Burning Wheel, Savage Worlds, GURPS, Dungeon World, True20, Fate, Primetime Adventures. Take your pick.
That said, best you can do is cap leveling at three.