I grew up pop up camper camping, then tenting, then in a pop up (I bought my parents' pop up), now back to a tent. I love camping in general.
I agree with everyone that you want a GOOD tent. Look for something with a rainfly that comes low on the tent. A dome type tent will hold up better in bad weather than a cabin tent, but there's a lot less space inside. We have a big dome tent that's a breeze to set up, a Columbia Bugaboo II (bought in the Cabela's bargain cave). We also have a giant Eureka Copper Canyon cabin tent. I love the cabin tent for its space, but it is a sail in a windstorm! You need about 100 stakes (Ok, more like 20) to hold it in place. My husband doesn't like to "rough it", though, and he is SO happy with the cabin tent. He likes it better than our old camper because there's so much room, and with our double high airbed, we can walk all the way around both sides of the bed. In our pop up, one of us had to climb over the other. Baby Z has been "camping" in the big tent in the yard with us and it was so nice to have space for her pack and play, a comfy chair, and all the necessities you need with a 2 month old baby. I have GOOD camping gear, but I don't pay full price. The Eureka tent came from the outlet store online. Most of my gear has been gifts, bought on sale, or secondhand.
I agree with everyone to try camping locally first. Borrow or rent gear (our local college rents out everything you need to go camping for wicked cheap!) and try it, even in the backyard.
Your main "Must haves":
-Tent
-tarp to put under the tent to protect the floor (this should be a tiny bit smaller than the tent itself so water doesn't collect. You can cut or fold a tarp to fit)
-something comfy to sleep on (airbed, camp pads, cot, etc.)
-Bedding like sleeping bags or blankets and sheets
-lighting (we have battery powered lights for inside the tent, and an oil lantern for outside)
-cooler for food
-stove and fuel, pots, pans (my pots and pans are all yard sale finds)
-dishes and utensils
-raincoats! I keep ponchos in our gear. It's no fun setting up or breaking camp in the rain. At least with a poncho you stay relatively dry.
If you have those things, you'll have the essentials. Other things that are nice:
-a tarp (with rope! Look up how to properly hang one on YouTube) or canopy to put up if it rains so you don't have to huddle in the tent
-plastic totes to put things in so they don't get wet if it rains (We keep our food in rubbermaid bins. It also keeps critters at bay. Put food in your vehicle at night if you can so a rascally raccoon doesn't steal your breakfast!)
-chairs
-stuff to do on a rainy night: games, books, cards, etc.
Plus you'll need all your toiletries, towels, clothes, etc. No hotel soap at a campground.
And I second the suggestion of a potty of some kind. It'll be a lifesaver with children. Heck, I don't like walking to the bathhouse at 2 AM either. We have a Luggable Loo for tenting. It's wicked basic, but functional and great in an emergency, too! (we have a septic tank that needs electricity to pump. Long power outage means no flushing!)