1/2 ton is good for a 22 foot trailer. But you would be better off with a 3/4 ton truck for a 30 foot trailer. You definitely want a towing package which should include a receiver and wiring, upgraded cooling including an external transmission cooler, towing mirrors and hopefully an integrated brake controller.
As far as your concern on the hitch, your 1/2 ton will probably not have the payload capacity (think about trailer tongue weight as well as weight of the gear in the bed here) to worry about which hitch you buy. Both the factory and the aftermarket will work fine for what you are going to tow.
I would ask about the rear axle gear ratio on the truck and stay away from things in the 3.5x or 3.4x or lower range. I would think you want at a minimum a 3.7x or even into the 4.x's to allow you to upgrade in the future.
Now go online and research a few trailer weights both for 22 foot and maybe 30 foot trailers. Take the advertised dry weights and add 1,000 pounds (Just a Wild A** Guess here). Now take 15 percent of that total. This represents the tongue weight of the trailer you are considering. Write these numbers down and take the list with you to the truck dealer.
At the dealer mostly ignore the huge towing capacity numbers in the brochure and just open the drivers door and look at the yellow sticker on the door jamb. This will give you the true capacity for that particular truck. Pay attention to the payload here as it will likely be surprisingly low. That payload number is based on a single 150 pound driver. Now add in your passengers weights. If you have kids they will get heavier as they get older. Maybe figure 200 lbs for every additional male and 125 lbs for every additional female. Subtract that number from the payload capacity. What about the weight distribution hitch, bicycles, firewood, extra water. Maybe go conservative and subtract an additional 150 pounds from the capacity.
Now you're left with the true capacity of the truck you are considering. This is where the size and therefore weight of the trailer comes in. Look at the list you brought with you and subtract the tongue weight from what just you calculated as the trucks payload number above. Does the truck you are considering have enough payload capacity to carry that tongue weight or are you hitting negative numbers?
Oh also, you are correct that the weight distribution hitch is an add on part and not part of the new truck.