Good recording equipment tends to be on the expensive side... Your question title talks about 4 microphones, your body about 6. Usually the most you get in one reasonable piece of equipment are 8 microphone inputs.
Now there are basically 2 approaches for recording in one take: have equipment useful for creating live mixes, or not. Equipment useful for live mixes is either an analog mixer or a soundcard with internal mixer which you control with a digital controller. The latter has the advantage that you can record the live mix settings as a starting setup and then do your final studio mix based on it. The former has the advantage that it's without monitoring delay, more reliable live and hands-on. Also, it's cheaper.
For 8channels+, only quite new USB equipment will work sensibly, and that's expensive. I lean more towards using good "vintage" equipment (in connection with computers, hardware ages a lot faster than studio stuff in general) where you tend to be better off with Firewire. Stuff like an Alesis iO|26 is mostly an audio interface (with some internal mixing) and you can connect D/A converters with ADAT output to it in order to get more input channels.
Driver situation is icky for discontinued products like this for Windows/MacOSX, and internal mixer support for Linux-supported devices tends to be spotty at most.
So my own version for multi-channel recording is a Mackie 1620 with Firewire interface. It has 8 mic and 8 line inputs and is not extensible. Driver situation with both newer MacOSX and Windows versions seems to have more or less collapsed, making it a reasonably affordable option under Linux (where it works well). There is no internal mixer, and playback options are limited (basically, just a two-channel mix). I use it with Ardour under Ubuntu Studio. It records with good quality right after the preamps, so the recording and the live mix are completely independent and you'll do the latter using a DAW.
In a typical band setting, you'll probably arrive soon in the situation that you'll use a submixer for getting the drummer enough mics.
So there are a lots of forwards and backs. Consider looking at Ubuntu Studio or other GNU/Linux distributions and some "vintage" equipment if you want good as well as cheap, and expect to be coursing the forums before and after buying in order to get it working well.
And check out Ardour. There is really no alternative when going the Linux route for serious multitrack recording so you probably should see whether you can get friendly with that first before choosing that path.