You need to be more specific with what you really want to do.
Desktops are cheaper than laptops.
When I hear sound card, I think - gaming sound card. What you need to look into is something external that can give you good recording and playback quality. For entry level recording gear, I usually point people to
www.m-audio.com . Take a look at their USB products.
Since you'll just be recording most often 1 vocalist at a time, on 1 mic, you can get something with 1 or 2 preamps on it. You'll find what you need at that site.
Furthermore, you can get 1 decent mic. I suggest a condensor, and make your own DIY Pop Filter (bend a hanger into a loop, and stick a pair of pantyhose over it - google it).
finally, the computer specs. Too broad to begin here if you don't know what software/plugins/samples you'll be using. Futhermore, we need a budget to work with.
Hope this helps, let us know more info.