That AKG D112 bass mic is preferred by a lot of pro drummers and engineers. So you can't go wrong there. Go with a Shure SM57 for the snare, it's another tried and true mic. Find a pair of large diaghram condensers on sale for overheads. That is, if you want the overheads to pick up the toms, too. If you plan on getting more mics in the future then you could go with small diaphram condensers, these will be better suited for only cymbals. You could also put one on the hi-hat.
You can get a great sound out of four mic's. I've made recordings with only three mics, a bass mic and two condenser overheads. I used the most affordable mics and mixer I could find (Samson Q-kick, Nady CM-88's, Behringer 1002) but you can hear everything ok. The snare is tuned high so it is still prominent even though it's not close-mic'ed: :http://www.youtube.com/w/Ryan%27s-Mo...?v=dkpexifMY9M
I ran the mix into a camcorder that didn't have the proper inputs, so it would have sounded fuller, louder, and all around better if I had ran it into an audio recorder of any kind.
So if you get three mics: that D112, and two nice overheads, you will be in business.