The built-in soundcard should be fine to get you started. I used mine for over a year before forking out for a better card. You will probably outgrow it if you get more serious about the quality or need more simultaneous inputs or outputs, but by that point you should have a good grasp on what you need to improve your sound.
The mics and preamps are the area where you seem to be lacking. A single 58 and some unknown generic mic aren't likely to get a great sound, regardless of the recording medium. And the only preamp you have to my knowledge is the one on the "mic" input on your soundcard (I'd avoid it unless you have no other choice: an external preamp to the line-in on your card is the way to go).
You could buy a budget single channel pre-amp for around $100, and use the 58 with it. You'd have to record the drums first with the 58 as an overhead and then dub in all the other instruments one at a time. If you do that right, it should beat the crap out of a pair of room mics for the whole band.
Better would be a small mixer (say, 4 channels) with built-in preamps, but that's probably out of your budget. And you'd need more mics to take advantage of it.
