Re: Decent stage mic
The Shure SM-57 is a good workhorse for saxophone . . . durable and road-worthy . . . personally, I prefer it over the SM-58 on saxophone.
However, if you're planning on something that can work for recording as well, you may want to drop a few extra bucks and consider the Sennheiser MD-421 or MD-441. I'm a fan of the MD-441, but there's nothing wrong with the MD-421 (I've used both for live and recording).
If you want a good affordable clip-on, try to get your hands on an AKG D-409 (when I go wired on stage, that's what I use) . . . they may be out of production now, but you can find them occasionally on eBay (I picked a couple up on eBay for $79 a piece) . . . it's a dynamic mic, and has a fatter and warmer sound than its condenser counterparts (C-409, C-419), plus it doesn't require phantom power. Of course, I wouldn't use it for recording . . .
Best of luck!