well.. basic recording tips and setups. I guess most on this topic has already been said, but to recap:
there's several ways to do it.
1 easy: get a standalone recorder like anything in the zoom family, from zoom h1 through zoom h4n works fine, even those with video camera's have superior audio.
This is really easy in setup and doesn't really have to be too costly, with the zoom h1 being only around 100 bucks.
Then put up some music in the background to play to and record it all in one take.
2 intermediate: get a decent usb microphone (or use a standalone setup as one, anything in the zoom series can be just plugged in as a good usb mic) and recording software like garageband or audacity. record it in seperate tracks on these programs. have 1 track for the background music and 1 track for your microphone input. beware! you may get a lag between the two tracks, so you have to allign them in post! so it's not necessarily you being off-tempo, it might be the lag/latency.
when recording in this setup always wear headphones so as not to leak background music into your recording!
3 hard: get a condenser mic (and a pop-filter), mic stand, a good audio interface, like the aforementioned m-audio fast track pro, beware though that the original is not compatible with windows 8 (I ran into this problem. Now i'm still using it on another w7 box xD). also get a good standalone limiter and or compressor. otherwise the condensor mic input will get blown out and distorted when playing with a large dynamic range. (at least, I always encountered this problem while singing in a high dynamic range, too soft and the gain too low and i wouldn't be heard on the recording and too hard and the gain still open from singing softly and the the input would get all distorted)
then process it through a good DAW like cubase vst, adobe soundbooth, fruityloops (=fl-studio) and the like.
instead of a condensor mic and mic stand with popfilter, you could also opt for a clip-on mic for saxophones i'd guess, though i have no experience with them.
a good dynamic mic may also do the trick btw, it's especially good to use instead of a condensor with popfilter and limiter and compressor. the shure sm 57is a decent one. I personally like the sm58 better as it's a little bit more versatile. it's basically the same mic but with a vocalist popfilter ontop. so with it it's a great vocal mic and after taking it off it's a 57 and great for recording (loud) instruments.
when recording in this setup always wear headphones so as not to leak background music into your recording!
hope this helps a bit.
as for my credentials: I've been looking into recording for a few years, done a short course and have tried a few things, though mainly use the first approach nowadays since i often record on the fly or during jamsessions. using the zoom h1 as a standalone.
as for processors like a limiter and compressor, i'm not sure if there are special saxophone ones, but I myself would try using vocal processors like those by TC-helicon. but i'm sure there is a lot of specialised equipment for that.
and i'm not affiliated to any of the products mentioned above. I just use them and like them.
