If you are going the mixer into interface route than the mixer will most likely have two sets of outputs. One will be called something like "mix out" and will have jack for left and right. The other set will be called something like "control room out" or "monitor out" and have the same left and right. Not all mixers have this but most do. If you get a 2x2 interface that means your interface will be capable of recording and playing back two tracks simultaneously. You need to be able to at least do 2 tracks simultaneously in order to record in stereo. You will connect a set of cables from the "mix out" jacks on the mixer into the interface's channel 1 and 2 (left and right) inputs. You will have several monitoring options. You can either connect your monitor speakers to the outputs on the interface (which is probably the best bet) or you can connect them to "control room out" or "monitor out" on the mixer. You could also use a set of RCA cables if your mixer has a 2 track out or something similar but balanced trs connections are best.
All that being said, if you really want to get by super duper cheap and quality doesn't matter too much to you you can connect a mixer directly into a PC's soundcard's line in (NOT the microphone jack. Most are mono and terrible) using either a 1/8" to RCA stereo adapter cable or a 1/8" to 1/4" splitter and forgo the interface but you probably wont be too happy with the results.
How I would do it for such a small kit is I would go ahead and take the plunge and grab a decent 4 in 4 out interface, a decent kick mic (pretty obvious what that's for), a Shure SM57 for the snare (there are better more custom tailored mics, but the SM57 is pretty much the one size fits all instrument mic and will work pretty well for just about anything and even if you score better mics later you will still find it useful), and a matched pair of omnidirectional mics (omnidirectional means they pick up more than just what's in front of them) and do all my mixing in software. You can always throw in more mics and a mixer later and having 4 independent channels will give you more control of the mix. Plus, once you get better at mixing up your drums you can get away with using 2 channels on the interface and do all of your mixing with an outboard mixer so you have two channels left over to record something else simultaneously (guitar scratch tracks, etc).
There are all kinds of youtube videos that show different micing techniques using 4 mics on a small kit. The general idea is to capture as much of the kit as you can with the overheads, pan them left and right to taste to create a wide stereo effect to give the kit a sense of space, and then bring the kick mic and snare mic in to add extra punch. There are a lot of different ways to get drums recorded and each has there own benefits and draw backs so experimentation is key.
Before we overlook it you are going to need some kind of DAW software to make all of this happen and the market is full of all kinds of different shit and they are all pretty good. If you get an MAudio interface it will most likely come with some lite version of Pro Tools. I would think that most interfaces come with some kind of DAW software. Reaper is a good starting point if you find Pro Tools to be to complicated (some people hate it) or you get an interface that comes with something crappy. And, though most of us hate too, READ THE MANUALS that comes with whatever software you choose.
