What exactly bent on the rear? Was the frame bent? There are not to many budget bikes active on this forum, but there definitely is a few. Get something that fits you, at size 5'8" a 54cm is going to fit probably the best. But being 16 you are very likely to grow, maybe get a 56cm sized frame. I suggest buying used, $200 is really the cheapest entry level you can go that is one step above a walmart bike. I'm sure you could get a fully working bike for $200 that is lose to $400/$500 new. Try and hook up with a local bike shop and see what they can do with getting you a used bike. I am afraid with you being so new to the sport that you might get ripped on an ebay bike.
Really sorry for your loss, don't feel afraid to be open. Usually people are supportive on these forums.