Since you don't have many replies, here is my take (although I am new here but I had tons of cars, pickups and couple of Jeeps before).
First - you have 3.8 L engine.
Change the oil right away - you don't know who change it and when.
Take your manual and use whatever weight Jeep recommends.
Go with synthetic. I am with Mobile 1 for the last 15 years and very happy.
I change mine every 5,000 ml.
Wash the Jeep (in and out). Wash it underneath. If it looks decent, either buy 3M undercarriage protection (like 3-4 cans) and spray the heck out of it, or take it to the pro, and do the protection.
With every Jeep, I do this :
I buy 3-4 cans of WD40, and I soak the inside of the doors with it (the rear gate as well). Spray the heck INSIDE of doors so when this drys out there will be nice layer of protection against any moist that will creep in.
As far as wax - you have tons of options out there. Rule of thumb - buy more expensive ones and you will be fine. I use Mothers and I love it.
As far as plastics go :
Stay away from Armor-all. Garbage. Shiny garbage which attracts dirt.
I am using some product from California. Forgot the name, and I am in the office now. Something like Black Max or something like that. Do the search here.
Hope this helps, and good luck with your new baby