combo amps (like the one you have) do everything in one piece. essentially made for convinience and simplicity.
half/full stacks are made of 2 essential pieces, a head and a cabinet. you plug into the head and then you plug into the cab. you can't use a cab without a head because the cab relies on the head's power amp and your tone relies on the combination of the preamp and power amp. sorry if that doesn't make much sense but i found it kinda hard to describe it. wikipedia could probably explain it better.
as for good brands, my personal favorites are engl and peavey but that's all based on preference. you might find that you like marshalls, or kranks, or what ever the fuck else. as for most of them being in your budget, probably not
