I am going to make the assumption your family have all been out camping together and all members enjoy camping and want to get into camping in a bigger way. Right? I say this because if you've never really tried it, you should before investing a lot of time and money into this past time ... because it's not for everybody.
Back to your initial question, conventional wisdom dictates finding the RV first which 1) meets your family's camping needs and; 2) identifying what you like in terms of floor plan and amenities.
Then, once you know the weight numbers of that unit (whether it be carrying or towing the RV), go find and match the right tow vehicle to do the job safely and with the appropriate power and set up (i.e. camper and/or tow package, upgraded suspension & tires etc.)
Similar to comments above, with two adults and three kids I question whether a truck camper (TC) is the right kind of RV for your family's camping needs. We downsized from a Class C that would sleep 6 comfortably including 4 kids inside and 4 outside in tents (when we used to have lots of kids come camping with us) to a truck camper after they all got older and moved on and we wanted to limit our camping experiences to just the two of us. The TC does all of that for us and people know it really only accommodates two people comfortably ... 3 total in a pinch.
Also, you'll need a minimum 3/4 ton truck for a TC whereas a well equipped and powered 1/2 ton can do a lot of pulling (i.e. travel trailer or hybrid). If you've not RV camped before, get to the RV shows or at least some dealers with all of your crew and try things out like beds, sitting in the dining area etc. ... also think about what you'll be doing if stuck inside during bad weather.
You might also want to try renting an RV for an outing or two to see what works and what doesn't for your needs. A more typical approach with a 5 person, young family is to start with a good, used tent trailer, figure out your routines and then step up into something else once you know what you want and need.
Good Luck and keep us posted.
