At 350# riding strictly on roads, I would stick to a non-suspension bike like a Trek 7.2, or a Giant Rapid, or equivalent hybrid commuter bike by Specialized, Fuji, or others. I wouldn't worry about breaking the frame. I ride a Masi Partenza road bike at 240#, and it holds up just fine. The most damage you will do to the bike is broken spokes, and those will happen mostly on the rear wheel, where 2/3 of the weight is distributed. Shocks absorb energy that would otherwise be propelling you forward. If you are going to do some serious rock-hopping off road biking, go with full suspension, otherwise I recommend hard tails and forks. You should be able to get something decent from a good bike shop for $400-$600.