Ive raced road bikes for years. How much do you plan on riding? Personally I would go to a bike shop and look at bikes, ask to be fitted on a bike. Keep track of the size frame that they put you on. Most companies are in CM sizes (56cm, 58cm etc... ) though some compaies use M,L, XL but they still list what dimensions the frames are.
Roadbikes are just like wakeboarding, theyre super expensive... Id say $350 is really stretching it unless youre looking at some old bike that is shaped like a road bike. Most entry level road bikes start out at around $750 or so, so i would say your looking closer in the $500 for a used bike. Check out your local bike shops, a lot of them do cosignment sales and sell trade ins sometimes. How tall are you?