There are a few threads about this -- a search of the forum should turn them up.
The short awnser is:
size and fit -- if you don't know what size you take there are resources online that should help narrow things down for you.
frame geometry and material -- do you want a comfy stable long distance ride (touring/sport touring) or a fast racy quick handling more twitchy ride (race bike). Some form of cromoly and butted is better than hi-tensile and straight gauge. For $200 you might find an old Cannondale (or similar) which would be an aluminum frame which would also be fine.
wheels with alloy rims and rather than steel
frame without crash damage or a lot of rust
Did I mention getting a bike that fits you.
What part of the county are you in? In some parts $200 for a road bike should give you lots of choice and in others that might get you a ready to ride Schwinn Varsity. (Nothing wrong with a Varsity, but it weights 2x what a standard road bike weight.)
If you are new to cycling I would concentrate on getting a solid bike to ride and train on, which will improve your fitness and speed, and then worry about getting a better/racier bike that could help make you competitive.
$200 isn't much of a budget, even for used. It will help if you can do your own mechanics though. I just bought an old Nishiki that wasn't in as good a shape as I thought. I paid $125 for the bike, which is okay, but by the time I got new tires (Gator Skins), cables, new headset, chain, cogset, bottom bracket and wheels serviced, I probably have about $400 in it.
I recently purchased an '87 Fuji for $40, steel frame road bike w/alloy wheels, nothing too special. It needed a scrubbing and a little work, new tires, new chain, brake and deraileur adjustments... mostly basic stuff. Afterwards, with a couple add-ons, I've spent a total of $130 and I love it. It's great for commuting and touring, IMHO. Another bonus of buying an older used bike, one that's not neccesarily in the best of shape... it provides you with the opportunity to do some wrench work. Performing a little maintenance (even a bit more) is great experience to have if you plan on doing a fair amount of biking. If you're looking for that sort of thing, anyway...
I live in the OP's area and there are bikes to be had for $100 - $120 but they are the bottom of the barrel or need a lot of work. Then there's the $200 - $225 bikes that are nicer frames w/ a little better components, ready to ride. It's funny that there doesn't seem to be a lot in between there.
$300 to $350 will get you a Reynolds or maybe low end Columbus Trek or Schwinn that's pretty tasty.
I would say to try and spend about $250 with a Craigs lister that knows what he is selling and has tuned the bike, added fresh cables, good tires and bar tape. If the seller just says, " it was my brothers bike and he left in the garage 5 years ago, not so good, unless it's a Colnago or DeRosa for $200. Hmm, In that case I would be on it already.
And make sure it fits you. !!!!!!!!! You see ads that say, "this is an adult bike" not very helpful in sizing.