Your dealer should be a lot of help in all this - no need to go it alone. With that, let me offer some thoughts to get you started.
The hitch weight will be well above 388 pounds. Hitch weight on TM's runs about 14% of the total ready-to-camp weight of the trailer. The ready-to-camp weight will be around 3500-3800 pounds, so hitch weight will be around 500 pounds round number. It is probably wise - and nothing will be hurt - by going bigger in all hitch-related items. You don't want to be towing with no margin.
With this change, your Class 3 weight distributing hitch, equipped with 800-pound spring bars, will be good. The shank of the WDH simply slides into the 2" hitch receiver that is presumably permanently mounted to the chassis of your Sorrento. No formal "installation" is needed, though there are a couple easy adjustments to be made. The WDH includes a ball mount which has an adjustable drop to match your vehicle - different vehicles need different drops.
There are many good WDHs. You almost certainly don't need one with sway control, since TMs are built not to sway. However, I personally recommend (others have different preferences) a trunnion-style WDH since you can add sway control at a later time if you feel you need it.
You'll find some useful info on this page
https://www.etrailer.com/question-365350.html
and more on this page
https://www.etrailer.com/dept-pg-Wei...ion_Hitch.aspx
If your Sorrento is pre-wired with a 7-pin connector near the hitch, you should be good to go. Stop lights, running lights, turn signals, 12-volt charge line, and ground will all be correct - they are standard. However, electric brakes and backup lights are sometimes unconnected, so you (your dealer) should confirm them. No need for any connection to the 4-pin connector that is probably nearby.
You will need an electric brake controller, properly wired to the 7-pin connector, unless the Sorrento has one built-in - unlikely unless one is included in an optional factory tow package.
Lots to think about, lots of questions. And lots of answers here on the forum - please ask.
Bill