Just a couple of thoughts about equipment:

Like you my Darling Bride thinks "roughing it" means staying at a hotel WITHOUT room service. Not long after we were married I took her camping for the first time. I had a great time, she didnt' and hasn't been back since.

Buy the basics tent, sleeping bags, lanterns and a stove.

Since you'll be camping at a state park there will probably be a decent bathroom/showerhouse but check it out beforehand. Nothing is going to make her more miserable than not being able to "freshen up".

For a tent (2 adults and 2 children) a minimum size would be 10X10. Get one that is at least 6' high. Being able to stand up in the tent is a big bonus while getting dressed for you and her. A dome style is the easiest to set up. Stick to the brand names (Coleman is fine) and try Wally World or Dicks Sporting Goods. Decent prices.

Make sure to get an air mattress (double or queen size) for you and her. You will sleep much better. Kids can use foam pads, they'll be fine. Make sure to take pillows.

Sleeping bags don't have to be too expensive. Coleman is fine. Might think about getting one big enough for you and her and seperate ones for the kids.

Lanterns and stove. Coleman again. I use their 2burner propane stove and propane lanterns. Easy to deal with and the fule bottles aren't that expensive.

Borrow kitchen supplies from the house.

As for bugs. Take bug spray and citronella candles.

Pick a weekend and go for it. If the wether forecast is for nasty rainy weather pick another weekend. Nothing will ruin the first trip maore than bad weather.

Have a great time and report back to us after your first adventure.