As for brands to go for and avoid, I'd say to go for Corsair, Bitfenix, and NZXT. Those brands make some of the best I've seen.
There aren't really any brands to avoid, but I'd steer clear of certain Raidmax towers. They're cheap, but what you get is lower than that. They've still got some good cases, like the Seiran, and Helios.
Sizes:
Mini-ITX
The smallest kind of case available, the most well-known Mini-ITX case is the Bitfenix Prodigy, and is widely considered one of the most modded mITX case ever. Very space efficient, but not the best option for airflow.
Micro-ATX
Small, not as small as mITX, but small.
Most Dell and HP home computers use this size.
Small, not as small as mITX, but small.
Most Dell and HP home computers use this size.
ATX-Mid
A good size for budget gamers and for small watercooling loops.
A good size for budget gamers and for small watercooling loops.
ATX-Full
Large, bulky, and most hardcore gamers and builders use this for huge watercooling loops, massive data towers, and crazy case mods.
Large, bulky, and most hardcore gamers and builders use this for huge watercooling loops, massive data towers, and crazy case mods.
ATX Test bench
Usually looking like a bunch of metal bars welded together to make a very open-aired mATX chassis, so that swapping parts and changing internals is very quick and easy. Not commonly used as a normal case.
Usually looking like a bunch of metal bars welded together to make a very open-aired mATX chassis, so that swapping parts and changing internals is very quick and easy. Not commonly used as a normal case.