I camp frequently and have been doing so for years.
You can do a first time trip without making a huge investment in equipment, if you want to.
If you plan to buy a tent, I recommend something big enough for your whole family, in case you plan future trips. My family has this tent, and it comfortably sleeps three, and we've used it on a dozen trips and I expect it to have ten more years of life in it at least.
http://store.eurekatent.com/products/967965/Sunrise_EX_4_Tent
You can spend less than that if you like, but this is a comfortable size for 3.
For sleeping on, we use foam floor mats (the kind you would use on a playroom floor) over air mattresses. If you want to skip buying a sleeping bag, bring quilts. One to put underneath you and then one each for on top.
A large container for water. A couple of gallon bottles are good -- you want to have water handy for washing hands, etc.