You're looking for a hitch
receiver.
They're all about the same. They all are rated for the Tundra's max towing capacity, so you might as well buy by price or by the quality of the paint.
I have a Draw-Tite. It works fine. Reese is the same company. Putnam is good, so are Hidden Hitch, U-Haul (same as Draw-Tite) and all the rest. Ignore the so-called Class ratings of the receivers. Go by the actual rating in pounds. Anything equal to or over 7200# is more than adequate.
No wiring is included with any of the receivers. You'll need to get that done at a local trailer or hitch shop. Draw-Tite (sold under several brand names) is one of the makers of the electrical adapters (you may need one, two, or three depending on the type of electrical hook up to your trailer).
If you tow a trailer with electric brakes, you'll do best with either a Tekonsha Prodigy brake controller or a Jordan Ultima brake controller...don't consider anything else, and really don't buy a Draw-Tite or Reese controller. I really like my Jordan
http://www.jordanbrake.com/
Unless you just want to tow a really light trailer...then all you need is a ball to put into the bumper, or maybe a step-down bracket to get the ball lower, plus the lighting wiring. Check a trailer or hitch dealer. Balls come in three diameters, 1-7/8", 2", 2-5/16", and different shank diameters and lengths. Get the one that fits.
Ken