minion is completely correct, as are all of the answers here, although some may be way off the topic of what you were asking (particularly a couple of early responses - maybe people dont' take the time to read questions sometimes, I don't know, but your question was very clear to me and I just enjoyed reading the completely irrelevant posts after for a little while).
Firstly - minion is right, don't buy that korg or anything like it if you are in a situation where you can use a computer instead (and have a fast, reliable computer that isn't currently crashing a lot).
Secondly - you will need an interface that gives you several mic inputs if you plan on skipping the mixer. If you plan on using a mixer (the board you're speaking of is probably a mixer or "mixing board") then having microphone inputs (as opposed to line inputs) on the computer's audio interface aren't terribly important (and can in fact get in the way) but it's still important to have an audio interface with plenty of multitrack inputs (just in this case without the extra expense and circuitry of additional mic preamps since those are now supplied by your outboard mixer if you go with a mixer).
Quick summary of a mixer in common usage for computer recording:
A mixer in recording is used to provide mic preamps (the things that convert your xlr mic connector's output to a pro-audio +10db standard line output), a pre-recording equalizer (or eq, for tone shaping, ie, treble, mid and bass controls at the very least to be useful), and the other common usage which is to take several mic inputs (for close mixing a drumset's individual drums for example + a couple of overheads for your cymbals and the entire set's ambience) and "mixing" those down to stereo two track with levels set to sound great and stereo panning. Sometimes the snare and kick drum are kept in separate tracks even still to allow you to change their individual levels, effects etc while mixing down on the computer at the end, a good idea if you have enough track inputs on your computer's audio interface. The mixer will have bus and/or aux outs, each output of which should be connected to a different input on your computer's audio interface (previously known as your "sound card" in the consumer world). Then your mics etc are connected to the mixer's mic inputs, each input on the mixer is set to output to a different aux or bus or whatever (exact technology doesn't matter for this introduction), again except for with drums where you will probably have the different drum mics all go to either 2 or 4 bus outputs of their own, even if you have 10 drum mics, just "mixed" together into a stereo output plus snare and kick separately if possible (the 2 or 4 output option...). You get your band to play, listen with monitors (or at least headphones) in isolation and play with levels and eqs on each track to make it sound like a perfect recording (as much as possible), then hit record on the pc and play your song.
WITHOUT a mixer, for example you might get a presonus firepod (a good example of a computer audio interface that comes with 8 mic pres (pres is short for preamps) built in and does 8 outputs to your computer by default, one for each mic input). So you don't use a mixing board, instead you use the fancy computer software for recording multitrack audio and editing/mixing it, and you adjust the levels and monitor it all with software control using the program's built-in virtual mixer (which looks like a mixer on your computer screen and does the same things more or less but is limited in inputs and outputs to what your hardware audio interface provides). The result is the same in the long run, at least on paper.
Software info for either mixerless or mixer based recording: popular examples of the multitrack audio recording software are sonar, cubase, logic, digital performer, nuendo, protools (which requires special hardware to run) and tons of others. they all provide multitrack recording and playback, virtual mixers, etc etc (as well as tons of features not discussed in my intro).
So pros and cons:
mixer based:
-traditional/old school
-looks cool cuz you have this big mixer on your desk hahaha
-allows generally more inputs which can be mixed down PRIOR to recording which can be useful for drums etc for example (but can be a drawback as well, not worth getting into here).
-allows pre-recording equing (tone controls) and even effects (effects here are not often a good idea, but can save time at least if desired)
-can provide higher quality mic pres than available in your computer's hardware audio interface (if any are provided at all)
-very expensive to get a good mixer, major maintenance is required (all mixers have parts die regularly, can you solder well?)
-takes lots of extra space, and generally speaking will not sound any better than a decent mixerless solution
-can actually add noise and other garbage to the signal chain before recording
mixerless:
-cheaper than buying a good interface plus good mixer
-but you do have to spend more on a computer audio interface since you need plenty of mic pres and generally you want good quality since this is the only hardware getting in the way of the sound you want
-much less desk space needed
-cleaner signal path = less noise or chance of noise and interference
-mixing is done in software, can be a pain in the ass to control unless you buy a hardware "control surface" (such as a mackie control or
a behringer bcf-2000) which looks like a mixer but really only controls the otherwise mouse-controlled faders etc in your software mixer on your computer
Now onto your audio interface - you'll probably need a firewire connector on your computer since most good multitrack audio interfaces have firewire output now, not usb or pci (although those do exist as well but are becoming rare). Won't get too into this now, hope this was helpful.
Personally, I go mixerless unless I need a mixer for extra inputs (such as with drums). I run a pro level home studio. It works for me. Everyone's different.
Cheers,
Sorry for the long post! Trying to be helpful, without rereading it I'm just going ot assume that I've gone way off base here and am probably contradicting myself and being very confusing. Sorry if that's true!
by the way, this is a superficial look at the recording process, I'm ignoring many features of computer recording and mixer recording each. One quicky I missed is that mixer recording makes using outboard hardware effects such as compressors much easier (although some mixerless systems are catching up in technology now with some basic mixer functions built in). However being mixerless you can still use all of the software plugins that replicate those hardware effects such as compressors, eqs, whatever. But that's a huge discussion on it's own - either way you dont' want that korg thing unless you MUST be portable in a single box solution.
