Desktop vs. Laptop -- I usually tell people to make sure you need a laptop before you buy one, since for the same money - you can usually get better equipment in a desktop. I usually see people who buy a laptop, and it will sit on the same desk 99% of the time (where a desktop could be sitting). So at least in my opinion, unless you will use a laptop as a laptop - desktops are always better.

Brand - It really does not matter too much these days - People will always have "bad" stories about certain brands, but most of the major brands are good these days. I get dell, and haven't had any issues. Actually just got a brand new Dell yesterday. Plenty of memory (the more the better), CPU - I was looking hard for at least a quad core since many games take advantage of more cores (ended up getting 6 core AMD myself)