Any number of bikes can be found in your price range, and style is really up to you, not us. Some things people demand in one part of the country aren't needed in another or are only needed part time, only you will know what you must have, and you might not know for sure what you need until you've been at it a little while. But still, what others have said is good; plus also remember that you will be out in the elements and get some clothes for yourself as well as stuff for the bike. Layers of warmth and a waterproof shell.