Terp - I ride a stock 2003(?) Trek 4300 that you should be able to find used on eBay or Craigslist for around $200 (I think new they're around $400). The only major change you'll need to make to any used bike you get is to replace the left crank arm (~$20) and make sure the wheels are trued (~$20 at a local bike shop). There are a number of similar bikes made by GT, Fuji, Specialized, and Cannondale but what you'd really want to get is something that's heavy steel.
I put my bike through a lot of stress and strain (fast, heavy riding on less than smooth roads) and haven't had any issues yet but I ride a low-end converted mountain bike. I'd steer clear of a Discount Store bike (i.e. Walmart, Target) due to your size, but they'd be fine for your kid; used is definitely the way to go for you though. If you want to go the used route let me know and I can send you some bikes to check out. By the way, check your PM inbox.