I'd start sauntering through bike shops looking for bikes. Don't be in a hurry. remember, you're buying not just the bike, but a relationship with the bike shop. If they're worth your patronage, they will find you a good bike in your price range.

for what it's worth, I rode a $10 3 speed garage sale bike which only had 2 working gears for about 3 years before I got serious enough to want and deserve a bike that actually worked right.

and welcome to TE!