We have tent camped at many of the Texas State Parks. If you go to the Texas Parks and Wildlife site, it will give you a map and you can choose which area you want to go to. Then it lists the parks and amenities. Many parks have cabins and lodges as well as the traditional camping/RV sites. A pretty park near the DFW area is Bonham State Park, but it doesn't have lodges. Oklahoma also has great state parks. Likewise, you can go to the state website and look up the parks and amenities. I'm sure Arkansas has something similar.
Many of the parks also offer summer programs (usually on weekends) for kids. The rangers will offer identifying animal tracks, recycle art classes, etc. Sometimes these are posted on the website. If not, be sure to ask when you check in. My kids (14 and 7) have loved these programs over the years and we've all learned something each time.
As far as what to pack: close-toed shoes and jeans for hiking or walking in the woods, flip-flops for showers, towels and wash cloths, extra changes of clothes, toiletries, flashlights. We pack a whistle for each girl. When they go to the play area or are playing around the campsite, they have the whistle on in case they get lost. Then they can hug a tree and blow their whistle until we find them. Keep the food simple if you're cooking - hot dogs, hamburgers, fresh fruit and veggies. Lots of water. Foil packets on coals are also an easy way to cook meals - wrap up chicken, thin sliced potatoes, and other veggies w/ a pat of butter (and whatever seasonings you like)in foil (seal and leave some air space) and put directly on the coals. Cooks in about 15 -20 min. We've camped in tents with both girls from the time they were about 1 year old. Both love camping! And each now helps with the set-up of camp as well as camp chores. =) Enjoy!