I have experience recording brass, however sax is not 'brass'.

I'll put a third vote in for the SM57, even for sax. I've recorded alto, tenor and soprano with it many times.
You can also use it for brass, vocals, even snare drum.
It's a workhorse and stays healthy through a lot of use for a lot of years. It's hard to kill one.

That said, as mentioned by others above; you'll need a pre-amp.
Focusrite was mentioned and is fine. Good stuff.

So is StudioProjects, which offers a litle more in the way of actual preamp options at the price point (like swappable tube, solid state/tube mix, tube drive) but it would require a way to get the (audio) signal into the computer from the preamp. This is OK if you already have another decent soundcard/interface.
If not, the Focusrites are good audio to USB units and likely the best cost-effective solution.

Be aware the entry level Focusrite unit (2i2) usually does not include a mixer applet for the computer, so going just one step up may offer valuable features not realized by a first time purchaser.
One thing to note with this 2i2 unit; if you plug a mic into channel 1 (the Left side) you hear it in the left speaker. This can be annoying .. sure I can drop one side of the headset (which is 'kinda' common when recording vocals), but if I plug a bass in and only hear it the left side it can be a bit disconcerting while recording, so thought I'd mention to a potential purchaser.

And yes; RealBand is likely a better way to go (or some other DAW you are comfortable in). BiaB CAN record audio, but RB can record 40 additional tracks of audio. Biab is a bit restrictive in this way. You don't have to delete a take in RB to record another one (then mix parts these extra parts together) .. BiaB is limited in how many 'takes' you can work with.

I do not work here, but the benefits are still awesome
Make your sound your own!