I didn't see this mentioned, but I am sure it was already:
A pair of Channel lock pliers!
I bought an "el cheapo" tool kit from Walmart years ago, it is pretty complete even with some electrical connectors. It has worked fine for years. It does include channel lock pliers, and a small level - which lets me double check leveling the trailer, but especially helps me to level the grill! Our portable grill is propane, with one part smooth griddle, and few things are more annoying than trying to cook eggs on a beautiful morning and they all run to one side of the grill.
Yes, also make sure you have what you need to change a camper tire. And make sure you do a "practice change" at your house! I found that the jack for my pickup truck works for my TT, but I had to buy the correct socket to fit the lug nuts.
Don't worry, the first couple years are spent buying "stuff" for your camper... then the next 8 years are spent removing all the stuff you don't actually need, lol!