I'd second all the above. I have a TR182 - flies at 155-165 knots depending on altitude and what mood it's in, on 14-15 gph. But with 4 adults it's limited to about 3 hours - say 500 miles - with sensible reserves - less if the adults in question are all fairly heavy. (I have never landed it with less than 1 hour of fuel in the tanks). Apart from being a bit faster than your requirements, it doesn't really meet them. It's fairly expensive, by 35-year old spam can standards, and not particularly cheap to operate.
Flying 4+ hours is hard work, for the pilot and passengers. I once took a 172 down to LA - 3 hours in each direction - and it was seriously tiring (and quite boring).
I'd rethink what you really need when you have a bit more experience. A fuel stop on those 550 mile journeys will make everyone a lot happier.