Is 34 inches your "cycling inseam" or your pants leg length?

Cycling inseam is when you take a thin book, wedge it as far as it will go between your legs and measure the distance to the ground. It's difficult to do this solo of course.

You're probably looking for something along the lines of a 58cm or 60cm (maybe, depends on what you prefer) road bike and if you can find a good used deal near you, you can stretch your purchasing dollar. Don't forget that you'll need a decent pair of shorts, a jersey maybe and a helmet, spare tubes, water bottles... all that jazz adds up.

I'd steer clear of wheels with fewer than 24 spokes in the rear but at 235 you shouldn't have too much to worry about with respect to bikes and durability. Just take care of your gear!