Is a tow capacity of 6,200-6,500 enough?

A 20' TT will typically weigh only 2500-3500 pounds empty. Add another 2000 for water, gear, people (in the vehicle). If your truck/SUV has a true towing capacity of 6500 pounds, you'd be fine. What you need to watch is the payload capacity. If the trailer weighs 5500 pounds loaded, it might have a hitch weight of 500 pounds or more, depending on the layout of the TT and how it's loaded. A small truck with a towing capacity of 6500 pounds that it PULLS may only have the capability to handle 1000 pounds of payload (extra weight sitting on the vehicle) including the hitch weight, driver/passengers, and any other luggage and gear within the vehicle. Using those numbers as an example, with two 250-pound humans and a 500-pound hitch weight, you just quickly added 1000 pounds to your vehicle and met your payload capacity without adding any additional people or gear.
Just pay attention to hitch weight specs on trailers, and the payload capacity of the vehicle you buy. Also, a quick upgrade should be the tires. Most trucks and SUV's come with P-rated tires. Ditch them and get some LT tires. The stock tires are the weakest link.