If the bike is in your predetermined price range, then it sounds like a good starter. You don't know what sort of geometry you like so you'll at least learn that you either like or don't like the geometry you bought. However, if you have back, wrist, or other similar issues, you may want to stay away from 'race' geometry, particularly riding a small frame for your size.
As far as what to look for on a used bike, here's my typical check list:
1. Trueness of rim boths laterally and vertically
2. Seatpost slides freely
3. Stem (assuming quill) slides freely
4. Bike shifts through all gears
5. Chain doesn't skip on rear cogs with decent pedal pressure
All of this can be accomplished in a matter of minutes. If anything fails, I'll ask for money off or pass on the bike (frozen seatposts are no fun).