I may be too late to get in on the thread, but I'll throw in my 2 cents anyway.
You can get away with a $300-400 bike, but if you stick with biking, you'll look to upgrade within a year. (I speak from my own experience here.) The bikes at that price point are relatively heavy and don't have very good components. Look for at least the Shimano Alivio level, and avoid Acera on down.
Once you get to about the $600-800 price level, you start getting lighter frames with better components, and you won't be as likely to have breakdowns, bad shifting, etc.
5'9" with a short inseam means a large frame is too large. Look for a medium, or something between 15"-17" frame size. For now, you're riding for fun and exercise, so you want a more upright position, anyway. At your weight, you'll be more comfortable with a little more upright, less aggressive position. Also, you want to take it camping and/or ride with the kids, so all these things pretty much eliminate a road frame for now.
So you've narrowed it down to a mountain or hybrid style. In your BikeForum thread, you mention looking at the Trek 3700, 4300, and 4500. Of those, I'd recommend the 4500 because of the better component spec. A fairly comparable bike is the Specialized Rockhopper.
Too bad you're not a bit taller. I've got a hardtail sitting in my garage that's not getting much use these days; the frame is a warranty replacement after the original frame broke a chainstay, and only has half a dozen rides on it.
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