4everfrio

Welcome. It's good to see a family wanting to go camping!
Inks Lake is a nice spot to camp with kiddos. You might want to get one of the cabins. The new ones have A/C, which is always nice. They are also centrally located in the park. The playgrounds are just across the road and the park store isn't that far away.
On buying a tent, if the ad says 2man tent , it will sleep one comfortablely.
6man will sleep 4 people with room for clothes and anything else. Purchase a tent with ample room. Before you know it, the kids will bringing along friends and the extra room will come in handy.
When you need to buy other gear, hit the garage and yard sales. One can buy stoves and lanterns for a fraction of the cost of a new one. Plus, they hardly ever wear out. Mantles are the main item to go wrong with lanterns. They are easily replaced.
Buy a tarp to go under the tent. It will help the floor last longer. Also, buy one ( 10 x 12 ) to go over the table in camp. Summer showers and morning dew can get alot of gear wet. Buy some nylon rope or parachute cord. Both are very strong and will hold a tarp very well. The rope can also be used for a clothes line.
This should help some. I hope that it will lead to many happy days outside. Good luck and happy camping!!