I hate it when I see other folks do it, but now I'm gonna do it, too.
For $7 over your budget (might be tax, too, depending on what state you live in), get this:
Amazon.com: Streamlight TLR-1 LED Rail Mounted: Home Improvement
I have two of these, and I like them a LOT. Bright, durable, long run time (for a fairly inexpensive weapon-mounted light), the TLR-1 is a great choice. I am not connected to the company that makes them, or any company that sells them; I'm just a happy customer. Check out the buyer ratings at the link above; 69 5-star ratings, 10 4-star ratings, and a single 3-star (who doesn't seem to know how to read instructions and mount it correctly). No 2- or 1-star ratings at all; that kind of buyer happiness is almost unheard of!
Streamlight also offers the cheaper TLR-3, but it uses the less-common CR2 battery, it's not quite as bright, and the main body along with one of the two mounting rails is plastic. Save up a few more bucks and get the much nicer TLR-1.