Lots of good suggestions on here. I agree with the folks that recommend keeping it relatively simple, since you're kind of testing the water. Since you're "base camping," you can buy/rent/borrow stuff that's not so highly engineered, and designed for backpacking, where weight and supreme dependability are of paramount concern - and price.
Do get a headlamp. You can spend as much as you want, but I got one quite cheap at Big Lots (an Energizer brand for $5). It's nice to be hands-free after the sun goes down, whether you're stepping away to relieve yourself in the bushes, or collecting firewood... Plus, they're nice to keep in your car should you ever have to work under the hood at night.
You can take pillows, but I just make my own using the stuff sack and some assorted clothes - and if it gets wet, you haven't ruined a decent pillow.
Take some flip flops, or something that's easy to slip in and out of when you need to step outside your tent in the middle of the night to relieve yourself.
I agree with the caution about the air mattresses - the wrong one can act as a heat sink and leave you shivering through the night, so check the average nighttime temperature in the area you'll be in. If you're in the Adirondacks, for example, and it gets down into the 40's (or even 50's) you might have a long, uncomfortable night. Keep an eye out for a Thermarest (or something similar - but if you buy a used inflatable one, make sure it doesn't leak air) - I would spring for something along those lines since they're always nice to have around the house anyway, in case you have someone crashing on the floor... or even to use as an exercise mat.
One of those two-burner Coleman-style portable grills (always nice to have for tailgating...). I would't bother with one of those white gas backpacking stoves (again, back to the cost thing).
Take several "stuff sacks." You can get a three-pack, of various sizes, at Walmart for quite cheap - and they're good for hanging (oh, take some length of nylon cord) food from branches at night. (Don't assume that just because you're in a campground with a bunch of other people that you won't have nocturnal visitors looking for freebies.)
Oh, one of those little Jawbone Jamboxes, or other bluetooth speaker things for playing music off your phone... But respect your neighbors after "quiet-time" (I went camping with a dude a few years ago that thought we should rock Judas Priest "Unleashed in the East" through his Harley's stereo at 11:00 on night - not cool - LOL).