Aye, everything that you buy on your account will stay on the actual account. You can swap computers as many times you want, since the games are linked to it. The only real issue is that it's boring and takes time to redownload all the games over and over, and having some of these games take up quite some space on the HDD.
You can buy garrys mod separate, but as mentioned, you do need a source game such as HL2, CSS or TF2 if I remember right. But you can buy garrys mod together with one of those games for an extra price.
