Yo Danmarg! First, you gave us no budget, which makes the question impossible to answer. I need some hardware, too, about $100,000 worth- more. But I'll try to look at minimal setups. First, I have good news and bad news. The good news is- you can record a bunch of channels simultanoeusly for cheap. Bad news- you can't mix or process them separately afterwards. If you use a mixer, you get a number of busses, generally an even number. A 10 X 2 mixer, for instance, has 2 busses, in other words, stereo, left and right. There are 10 inputs. Each one can be panned so it comes out of the left, the right, or some combination therof. Note that in general, not all of those inputs will be mic inputs. That would be the 3-pin XLR inputs. There will be other inputs for line level stuff from outboard preamps or modelers, or maybe even a high-z input for unprocessed guitar or bass tracks. So you can take however many drum tracks you have, and combine them into 2, left and right. If you decide later that the snare is too loud, you can't change it. You have to get it right the first time. That rarely happens.
With most cheap digital recorders, you can only record 2 tracks at a time- same deal. You are going to need a minimum of 4 tracks, 6 or 8 would be better. To do that, any way you slice it, you are looking at money. In the PC version, you need a soundcard that has at least 4-6 line level unputs, and several channels of preamp. Assuming you're doing this for cheap, this is how I would start. First, you need a soundcard with at least 4 line level inputs. Many people like M-Audio Audiophile 2496- $100 or so. That's 4 inputs- 6 is much harder and more expensive. You already have a mixer, so there's 2 channels of preamp (2 busses- the left and right main outs). You need 2 more. I like M-Audio DMP-3- $150 or so. That's 2 relatively clean solid state channels with lots of gain. For this setup, you need 4 mics. 2 small diaphragm condenser mics for overheads, a cheap dynamic for snare, and a dedicated low frequency mic for kick. For overheads, I like MXL 604. $200 for a matched (more or less) pair. For snare, Shure SM57 has been working for a lot of people for years.-$80. I prefer a lot of other cheap mics, such as Sennheiser e835, but that's just me. For kick, you'll find as many opinions as there are fleas on a dog. For cheap, it's hard to beat Audio-Technica Pro 25 $60.
OK, before anybody jumps down my throat for recommending some cheapass gear, as I said, you didn't give is a budget, and you didn't tell us what mixer you are using. If it has more than 2 busses, you may already have 4 or more basic preamps. Be advised that I could spec out the same package for 12 mics or so, with high end mics and preamps, so the total cost would be
well over $20,000. Would all that high end gear sound better? Probably. But- it might be that all that high end gear would do is reveal that your room sucks in glorious detail. If your budget is a little higher, I could recommend modest upgrades in preamps and mics. Best of luck-Richie