Electrical hook up is as simple as plugging the standard "shorepower" cord into the post at the campsite. Water is as simple as connecting that white hose.
Sewer hookup is similar. Use the dealer's overpriced "starter" kit hose until you get some experience as there are dozens of options including a macerator pump like we use. Black (toilet) tank valve should remain Closed until at least 3/4 full (or you depart); grey (sink/shower) tank valve can remain open until the last night; use it to rinse the hose after you dump the black tank.
A Ford Expedition EL (extended wheelbase) will handle your trailer and family easily. The 3 big dogs would get their own 3d row seat
or the area behind the 2d row. Standard wheelbase model like I have will work if you don't carry a lot of "camping stuff" in the cargo area.
In my neighborhood
Pocahontas State Park is a great place to learn to camp. Close enough to Richmond (and Fort Lee) for all those things you determine you need after you're on site. Richmond Zoo, dozens of battlefields, RV dealers, Walmart, Home Depot, etc. a few minutes away. Less than 3 hour drive so you'll feel you went somewhere.
-- Chuck