Thank you everyone for your insights.
It's good to hear that the communities are usually very friendly, welcoming, and active. Thank you. If we decide to, I will ask about a buddy program for civilians. Right now we live in an area with mostly dual-income families or older couples with grown kids, so having more at-home spouses and young children as neighbors would be a pleasant change.
Yes, the housing is privatized. I think we can go check it out; they occasionally have an open house for housing so we will try to catch one. We can ask about the PX, school, lease and whatnot then. We can't really break our lease here (we would potentially end up owing the entire remainder of the rent anyway) so that's why I am wondering about it so much.
The base is in the greater Chesapeake region, so not really remote in the sense that it is days away from all civilization. It is remote in the sense that there isn't really a town. There is a grocery store, a few gas stations, a few doctor's offices and a chain restaurant or two. But all other amenities in that area are located on base (library, school, park/playgrounds, community pool or rec center, bowling alley, movie theatre). So, groceries and gas, fine. Anything else, nope. If we moved to that area off base, we would have to drive 40+ minutes to do anything because my daughter and I would not be allowed on base. So it seems like if we are going to move to that area, we would really be better on base. Or we could be ~40 minutes away and he has a commute, but we have everything we could ever want within a few minutes walk or drive. That's the choice we are facing, basically.
Checking in visitors at the gate sounds annoying, but oh well it's pretty far from any friends and family so probably won't happen too often. As long as they are allowed. Hopefully a few overnight visitors are ok too without all the permission hassle. I will definitely ask.
The base has a basic medical center, but it specifies for Tricare enrollees (which we do not have), and no emergency care so I don't know if they would see us at all. No urgent or emergency care in the nearby area, either, just some family physicians and dentists.
I have a good list of questions to ask the housing company now so we can decide and apply. Thanks all for your answers!