I don't remember any cradle charging floody light around that price range.
There's a Dorcy light or two that is cradle charged and withing your price range. It's a very throwy light though so you will probably need to use a diffuser.
There are a bunch of good cradle-rechargeables above $50 (streamlight, surefire, inova, pelican etc.) but none I've come across under $50 that fit the bill.
Longest time between use or longest runtime for the light?
I'm guessing the first one. If yes, look at low self discharge NiMh batteries or Li-ion batteries. Both should last at least a year with more then usable charge left.
Do understand that like LEDs, battery technology is also improving and changing rapidly, so spend some time over in the "Flashlight electronics, batteries included" forum to get the most up to date information.
One other point. I think many CPFers will agree.... it's worth it to go ahead and buy premium rechargeable cells to start with, especially if you go with lithium-ion cells. They will generally perform better, have better quality control, and have less chances of problems down the road.