Gerry pretty much answered your question. Pay special attention that the GROSS weight is the number to remember when looking for a truck.
1/2 ton trucks (Ford F-150, Chevy/GMC 1500, Dodge 1500, Nissan Titan or Toyota Tundras) only tow up to about 8,000 lbs. Newer models may go higher, but don't push it. You'll find that it's better to have more truck than what you need because you have to consider cargo, gear and passengers.
3/4 ton trucks, Ford F250, Chevy/GMC & Dodge 2500s can tow up to 12,000 lbs properly equipped. This is about where you lose the Japanese truck makers and from here on up, it's all American made. You can tow most TTs or small fifth wheels.
1 ton gets you up to about 14,000 to 15,000 for fifth wheels comfortably but bumper tow is about the same as 3/4 ton but the big difference is the 1 ton truck can carry a lot more on the rear axle which translates to the fifth wheel's pin weight.
Finally, the duallies are the big beasts of the recreational towing world. Of course, theres the MDTs and Semi Tractors after that.
NEVER allow a sales guy to sell you a trailer that is heavier than your weight rating, then tell you "just don't fill it up with stuff". If there's room for it, you'll put it in the rig and this doesn't work for keeping the weight down. If any salesman pushes that, then go find yourself another salesman or even dealer (I hold the dealer responsible for whatever shenanigans their salesmen try and pull). If they succeed, it becomes your problem and liability! Things break when you are within weight ratings, why push it!