At present, my best sax and non-orchestral brass instruments are in Kontakt libraries and, unfortunately for your "inexpensive" qualification, mostly for the full version of Kontakt and not the free Player version. What Rob Aylestone posted above is very telling about sax libraries and I'd add that some sound very synthetic throughout their entire range, some sound good within a given range, some can do some things better than an accomplished (maybe any) player can, many can sound good mixed in a section but not so good solo, they're getting better, and, not surprisingly, none appear to be as facile or versatile as an actual player---so, what TalismanRich alluded to really applies: it takes work and skill to use a sax library to get a realistic sound, especially as a solo/feature instrument.
All that being said, your least expensive alternatives might be free online loops and/or loop/sound services like Arcade, sounds.com, loopcloud, etc.
Good luck,
Paj
8^)