I love that you're going to give this a try :) I wish you the best.
I've backpacked or camped in pretty much every state park in pennsylvania. And for a (relatively) newcomer I would say Raccoon Creek State Park. It's close to Pit. The "rustic campsites" are where I camped and basically it's an open field in the woods, with a short walk to bathrooms and a water pump. It's flat, so taking a 5 year old hiking when you're bored means a nice leisurely walk in the woods without the "wow-I-thought-I-was-in-shape-but-now-I-want-to-die" kind of hills. That's if you want to borrow a tent. In this same area they have wooden shelters (wooden deck, roof, sides but open in front) that you can stay in, but they creep me out a little. I like to zip up my tent against the creepy crawlies. Picnic table and fire ring are there as well.
They have modern cabins you can rent too, if that's more your thing. They have much more amenities.
OR you can go for a yurt. I don't think they have any at Raccoon Creek but I think maybe Ohiopyle has them. These also have modern amenities, but they kinda look like a giant tent. Maybe that would be a good middle ground?
Check out the DCNR website and feel free to PM me if you have any questions about a specific park.