Crow, you really are looking for a touring bike. If it's a matter of budget, you can keep an eye out for a used Trek 520 or the like. I weigh about 330 right now,
and my Surly Long-Haul-Trucker hasn't had any problem supporting me, but I'm pretty easy on the equipment on everything other than weight... no hucking or curb
hopping in my current condition.
The Kona in my earlier pic also carries me fine, being a road-outfitted cyclocross bike, though for a more complete mount for your purposes, I'd probably swap the front crankset for a triple so I'd have that granny range available. The way its set up was fine even in the hilliest country, when I was fit... but now, it's still pretty good for flats and gentle rolling hill country.
As for wheels, you're looking for at least 32 spokes, and the biggest weakness in wheels for our needs is that machine-built wheels seem to have minor flaws in assembly... not noticeable for folks who don't put a lot of weight on 'em, but for us... yeah. A touring bike or cyclocross wheel should work fine, but I recommend that you get a real bike mechanic to re-lace the thing. If you want to go as far as I did with Jake (I used to bunny hop a lot of roadkill), have the wheel re-laced with DT or Wheelsmith double-butted spokes. The thinner inner length of the spoke with "give" a little where a straight gauge spoke will fatigue and break. I get some argument on that, but since I had it done, I haven't lost a single spoke. Also, for heavier loads, you want higher pressure in the tires. Otherwise pinch flats will bugger up your day.
Few bike companies will admit to their bikes holding our weight, probably for liability reasons, and the lighter racing type bikes just ain't built for us uber-Clydesdales.
City bikes are nice for short trips, but I wouldn't want to spend a lot of time on one, like on a longer trip. They'd be great for initial weight-loss work, though, and can be traded up for a more specialized type ride later (or keep it around as a local clunker bike... you can never have too many bikes!). The trikes are neat, but unless all your rides are from your driveway, they can be a pain to cart around, and when it's a pain to get your bike to the trail, it's *real* easy to come up with excuses not to ride.
There's been a lot of argument over the solid tires. No, they don't flat like a pneumatic, but I also think they feel dead... and they're very heavy compared to air-filled meats. With a little practice, the average flat will take just a few minutes to fix and you'll be on your way. Also, on a bugout or longer tour, kevlar-beaded tires can be packed as spares, for the unlikely event that a tire is badly damaged (which could easily take a solid-rubbered bike out of service). That being said, I've considered mounting a couple wheels with airless tires for my Montague and keeping them handy, just in case. If I get a better mtn. bike in the future, I might just slap 'em on
the Monty and leave 'em on, as that bike is quite solid and not nearly as lively as my old Cannondale was anyway. That's another option for you, by the way. The Montague Paratrooper is a VERY solid bike, and should easily be able to schlep you around while you pedal those extra pounds off.
It won't be as fast or poetic as a nice road bike, but it'll get you there without a lot of drama.
...and it folds up to fit in your trunk.