well the first thing to remember is to take your time! Wait until you get a perfect mix, not just an okay one...first impressions cannot be made again! (unless you use a different dj name hehe). So to start, let's review all of the outputs that you have on your mixer, you have booth, which is ment for the club monitors at a party. The second is master out, which is goes to the main club speakers. The record out is the output you should use for recording. Usually it's the best or tied with the best output on the mixer and on some mixers (djm-600) its volume is independant of the master volumes. Then with the proper cord you can plug in the RCA cord into your 1/8" stereo line in on your MD. From here you can transfer it to your computer, and track and burn it to cd using NERO burning rom or CD-R WIN. I prefer NERO.

Use the record output.
As for how to record, I'd say depends on some aspects. I'd say if it's mainly for practice, the MD is good. Record everything and listen to it. You'll learn a lot by doing that. I know a lot of guys that can mix well, and then when they press the record button they f*ck up real bad. When you are used to constant recording, that "stress factor" will be gone.

If you wanna make a mix cd, and you have the harddrive space (and a good recording program, like cool edit or soundforge) I'd say it's better to record straight to your computer (especially if you're also planning to make mp3's of it). If you record on MD first, there's already some compression. Transfer from your MD to your comp is likely to be done analog, so there will be a minimal amount of noise added. So you see, if you wanted to make the cleanest mp3 or cd, you already lost some quality in the process.
Also if you want to make a "pro" sounding mixcd, a little mastering would be welcome too (can also be done with progs like Soundforge and the likes).
As to burn, Nero is a good choice. Some of those recording/editing progs have burning capabilities too (Wavelab, Samplitude). If you want to make a cd with one long mix, but where you can still skip tracks (so one continuous signal, without 2s pause between each index), be sure both your cdburner and burning prog can do Disc-at-Once burning (Nero can, Samplitude can, soundforge can't, ...)

Jesus Christ, that's some awesome help! I appreciate it, DJ Thy. One short question, though: how do I hook up the sound output from the mixer directly to the computer?

___________________
Melodic Progressive.

Better than sex.

Well if you have a "normal" sound card (you need at least a line-in), you'll use the same cable as for the Minidisc. RCA to minijack. RCA from your mixer, to the line input (I said line, not mic, not the same levels) of your soundcard.

Then all you need is a decent recording proggie (dunno, the Soundrecorder that comes with Windows has some sort of record limit). Good examples are : Cool Edit, Sound Forge, Samplitude, Wavelab, Goldwave (shareware).
Those ones have lots of editing options too.

If you want to get a free soft (but you need a pretty strong comp for it), you could download the FREE (yes, free) version of Protools (http://www.digidesign.com). Protools is a software that is used in many studio's in the world. The recording method in the free version is a little bit awkward (if you want to do a stereo recording, you need to make two mono tracks (and one stereo master), pan 1 hard left, the other hard right, and record that way (and to get your final wav, you need to bounce it).
I prefer using the "normal" sound editors (like the first I mentioned), but hey, it's free