To give you a thought, my husband and I both grew up with a pool and my sister has one now, and I would not put one in based on those experiences. As nice as it was to have our own pool as kids, we had no one to play with unless we invited people over. Meanwhile, all my friends were at the public pool with classmates to play with. My sister's girls only have each other to play with, except for one family that has made my sister's pool their pool every summer -- the girls are never invited to their house reciprocally, they just invite themselves over every day. In addition, my sister pays around $800 to close their pool every summer (the pipes have to be flushed out a special way), and I don't know how much more in maintenance. Their property is wooded, so she complains about frogs and snakes and spiders in the pool constantly. And it was one of my chores to vacuum the pool, skim it, and chlorinate it when I was a kid. Things are a little more automated now, but I always hated the work. Now, I pay $360 every summer to drive five minutes, have a ton of friends for my kids to play with, and leave again without looking back. Yes, there are a lot of downsides to a public pool and upsides to having your own, but you asked for things to think about -- those would be my contributions.
If you do choose to get a pool, consider a salt water pool -- my brother has one and loves it -- no chlorination needed (although he's in Florida, so I don't know if that makes a difference).