Either of the WDH's you describe will do the job. The chain type is more commonly seen, but it requires an additional sway control device. The combination, however is somewhat cheaper than what I have, which is the Equal-I-Zer hitch. This uses heavy bars that are placed on L-brackets on the trailer tongue and it controls sway through friction at those points.
Reese is a manufacturer of popular chain type hitches.
I personally recommend the Tekonsha P3 brake controller. It is only about $20 more than the P2, which is also a popular choice, but it is much easier to set up properly and, because it uses electronic controls, it is not likely to be accidentally turned off (like my P2 once was when someone at the car dealership must have bumped a switch). For $30 less than the P2, you can buy the Tekonsha Primus, and it will work too.
If you don't mind spending installation fees, the trailer dealership will probably mount the WDH and sway control for you as well as the brake controller. Either one is fairly easy to set up, once you've done it, but the first time is a bit like cub scouts setting up a pup tent.
Edit: Your tow vehicle will be running very close to its limits with that trailer. I'd get the 600# tongue weight hitch and you're going to have to watch the weight you put into the trailer with that one. Ideal tongue weight should be between 12-15% of the trailer weight, so if you were to load the trailer to 5000#, the tongue weight could be as high as 750. That would require an 800# hitch. But, that loading would likely overload your tow vehicle. I think you should plan for a tow vehicle upgrade in the future.
- Jack