At one point I outweighed you by 100 pounds. These days I'm going about 250 and I attribute a lot of that to time on a bike.
I did my heavyweight riding on a steel-frame hybrid with 700c wheels (more road-oriented than mountain bike.) I had to replace the rear wheel with a double-wall rim because I kept popping spokes. Other than that, I had no problems.
If I were you, I'd avoid the Wal-Mart bikes. They tend to be poorly assembled and junky. Better to buy a good used bike or something low in the line of a reputable manufacturer. I know, for example, that here in Chicago you can easily buy a low-end Trek MTB or hybrid well within your price range.
Good luck.