There are several ratings you (may) need to consider:
Tow rating--the maximum weight of something you tow (4500 lbs apparently).
Trailer hitch rating--it may be less than the vehicle's tow rating, in which case the hitch may need to be upgraded.
Trailer hitch tongue weight rating--trailer tongue weight must be less than this. Often a trailer hitch will have a tongue weight rating that's 10% of its towed weight rating.
GVWR (gross vehicle weight rating) of the tow vehicle--the maximum for the combined weights of the vehicle, the occupants and cargo, and the tongue weight of the trailer.
GCWR (gross combined weight rating) of the tow vehicle--the maximum for the combined weights of the vehicle and its contents and the trailer and its contents, or stated another way, the total weight of the entire rig. Note that very often the GCWR is less than the sum of the GVWR and the maximum trailer weight rating for a vehicle, meaning that you cannot simultaneously have a fully-loaded vehicle and a heavy trailer.
GAWR (gross axle weight rating)--the maximum weight on the specified axle. When towing a trailer without a weight distributing hitch, the tongue weight is applied to the rear axle--and indeed causes more or less weight shift from the front to the rear as well depending on how far in back of the rear axle the tow ball is. A weight distributing hitch is designed to apply a torque such that the tongue weight is more evenly applied to both tow vehicle axles.
Tire weight ratings--similar to GAWRs, but sometimes they're a limiting factor rather than the axle weight rating, especially if the tires have been changed from the factory size or type.
Some vehicles also have a trailer frontal area limit specified.
It's usually wise to avoid picking the absolute biggest RV you can tow with your tow vehicle for a couple reasons. First, towing when you're not right at the limits is easier and safer and more comfortable, and with an RV you'll generally be going a good bit farther than across town to the dump or whatever. And second, travel trailers have a lot of frontal area and hence air resistance, and so are harder to pull at speed than many other commonly-towed things.
I suspect you'll be most limited by the GVWR or rear GAWR and the tongue weight of a trailer, doubly so if you'll be going as a family or other group of people rather than a single person or couple.
