I suggest you and your family start looking at a lot of RVs, pop up trailers, hybrid trailers, travel trailers, fifth wheels and motorhomes. Survey the costs of new and used units. Then, determine what will work with your budget....make sure you know what your vehicle will tow OR the cost of a new/used tow vehicle.
You have to determine what minimum items you want....very important in terms of having toilet facilities and/or a shower. Can you deal with wet bunkends that need to be dryed out when you get home if you have a pop-up or hybrid trailer.
In our case, we started with a used pop-up back in 1988 when our boys were 4 & 8. We were both teachers, so the income didn't allow for an expensive purchase and a pop-up was a very affordable solution. My wife was happy as long as beds were high & dry. We camped in a lot of NY state campgrounds, and we didn't mind using public toilets/showers although we did have a port-a-potty for when it was needed. We upgraded from a 8' box, to 10' and finally a 12' box which we kept for 10 years. We did a lot of camping and traveling in our pop-ups....made it out to Mount Rushmore and other states including Massachusetts, Pennsylvania, Maryland, and Virginia. As the boys were headed to college, we bought a 29' travel trailer which we used for 10 years, and now we have our 26'9" Minnie which serves our budget and travel needs.
If I were starting out today, I would probably want either a pop-up or hybrid that has a toilet & shower. Camping has become very popular, so a lot of facilities aren't always maintained to the degree that I would want my family to have to use them. Hybrids can have a lot of room for sleeping but still be towed with a larger SUV or 1/2 ton truck. Larger pop-ups may not be that less costly and weigh nearly as much. There's a lot to be said for the feeling of sleeping in a tent and enjoying the fresh air (as long as it's not too hot!).
If you can't store an rv at home or have place where you can let it dry out for a day or so after returning with wet bunkends, then a self contained travel trailer will be the least costly solution. For a bit more, fifth wheel trailers offer some advantages but as you get bigger, you're looking at a 3/4 ton pick up for a tow vehicle.
Then, you can always look at motorhomes.
For your first purchase, consider buying something slightly used because if you decide to sell it (whether you don't like rving or want something different), you should be able to minimize any financial loss. And, you need to camp and travel for a year or so to see what you would really like to have and what you don't need. I'd rather have a more modest rig and be able to travel than have a rig I can't afford to take out whenever I want to.
Although the suggestions for renting an RV is a good one, I'm not sure whether it is that easy to rent a pop-up, hybrid, TT or FW. If you are considering a Class C or motor home, than renting one first is definitely a good idea.
Finally...learn ahead of time all of the things you need to know about towing....determining what vehicle can safely tow. You have to be very careful about advertised towing capacities i.e. my Tundra can technically tow 10,000 lbs. but the payload capacity drops that figure to 7,500 or so. I'm towing around 6,400 lbs. and wouldn't want to tow any more weight unless I were to upgrade to a 3/4 ton pick-up truck.
Take your time, and I hope it works out for you!