To get the most out of it you'd be looking at a dSLR with stablised sensor. That rules out Canon or Nikon - whilst this lens would be great on either, you'd need a tripod for long shots, which rather contradicts your desire for a minimal kit with ultrazoom lens.
Cheapest 10MP camera with stablised sensor is Sony A100. Pentax K10D is perhaps $200 more, is waterproof but quite a bit heavier. Samsung GX10 (I think it's called) is same as Pentax but $100 less. There's also 6megapixel Pentax with stabilised sensor.
There's a new Olympus with stabilised sensor, E510 but its sensor is smaller and I don't know the Tamron fits it (and you'd lose the wide angle). I did hear there is going to be a new Leica 10x zoom for the new Olympus but would cost $1000 so rather counts that one out.
I have the Sony and it's great - stabilisation fantastic alternative to a tripod and would love the 18-250. As a "prosumer" upgrade to effectively a very high quality point and shoot you can't go wrong. Just remember that unlike point-and-shoot digitals, there is no "live preview" on the LCD screen, ie you don't see anything on the screen until you have taken the shot, and you must use the viewfinder. Except that the E510 Oly does have live preview so breaks all the dslr rules and will attract quite a following for that reason alone.
Also remember that cameras that shake the sensor can remove dust quite effectively - the bugbear of dslrs. Admittedly if you stick to one lens you shouldn't be getting dust onto the sensor but it's nice to have a self-cleaning camera.