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You are correct, the weight of the class III hitch reciever is included in the truck weight.

Tongue weight is the weight from the trailer that is not supported on the trailer axles. If you tried to lift the trailer by the tongue, the amount of weight you would have to lift is the tongue weight. It should be 10-15% of the total weight of the trailer and is usually listed in the trailer brochure. If you don't have the brochure, you can determine the weight by going to a certified scale and weighing the truck on it's own, and then with the trailer attached. Make sure the equalizer bars are loose when taking this measurement and also make sure the trailer wheels are not on the scale. The difference between the measurements is your tongue weight. After you get your measurement, you can tighten your equalizer bars back up and get another reading. That will tell you how much weight is really on your truck ( about 1/3 of the weight should go back to the trailer when you tighten the bars up ) when you are traveling so you can be sure you are within the gvwr of the truck.

I usually get these measurements at a landscape supply house on a wednesday afternoon. They are usually not busy and they allow me to keep their scale tied up for 5-10 minutes. They usually charge me about $0-$10.

And yes, you should get the largest weight distribution bars you can get, as long as the tongue on your trailer can support them. Some lightweight c channel or small box frames can only take 750 or 1000# bars.