Welcome to Sailnet.
Do your homework. Then do some more.
You don't mention actually knowing how to sail. Do you want a sailboat or a powerboat? You just say "boat." Do you want to get underway or just live on it in the marina? Probably you should start there because each has different maintenance issues. Both may have an engine, sure, but sailboats have rigging
and other stuff a powerboat doesn't.
You mentioned a mooring. There won't be electricity on a mooring ball.
Also, with kids, you'll want to be extra safety-conscious. Check out the Liveaboard section in this forum and in particular the threads about kids on board. Personally I think kids growing up on boats are just as or even more well-adjusted than those brought up in houses.
I'm not in your shoes, but if I was, I'd try not to stress out about it because the kids will sense that. If you can, turn it into an adventure and a learning experience with them. Include them, if you can, in some of the decision making (at least the 9 year old).
I've had kids as young as ten in my boating courses and they do fantastic. It's always fun to be surprised by how much they retain.
I can't end without highly recommending a safe boating course.
Good luck on your journey and have fun with it!!