You haven't told us any specs of your current computer or what software you're using. But if you're thinking of getting a new one......
Anything dual core is fine, but the Intel Core 2 Duos generally perform better than the AMD Turion X2. 1 GB RAM should be fine unless you have a lot of virtual instruments going at once. If at all possible, try to stick with Windows XP or Mac OS X. Windows Vista is generally not good for audio production just yet, and you would definitely need 2 GB RAM. Also, recording to an external Firewire 7200 RPM hard drive will allow you to use many more tracks.