"Also my teenage daughter's interested in going. Is it a "family-friendly" kind of experience?"
IF she is well behaved, polite, sticks WITH YOU, asks to see or touch, etc., they can be very friendly. If she acts like a semi-housebroken animal, then not so. If this is your first gun show, make sure to take your wife also. She will play a critical role in HOLDING YOUR WALLET for you. This may keep you from wasting money. Don't ask me how I know that. Also, you don't have to buy the first <whatever> you see.
My advice is to get the handgun first. You already have the permit, and if there is any kind of panic starting, handguns may be unavailable or priced out of your market. If you have decided on a Glock, for example, read everything you can about the gun, including what their going price is. Know what the variations are, the weaknesses of the gun are, what a worn (but still serviceable) gun looks like, etc., etc. If you can, take a more experienced friend with you, this would be to your advantages.
Just remember, "let the buyer beware". A lady friend of mine was once offered $100 for her M-1 Garand - "see, it has 'NM' stamped on it - that means 'new manufacture', so it isn't as valuable..." She is a competitive shooter, and was looking for parts for her M-1 National Match, a sophisticated target rifle. Needless to say, words were exchanged.
My advice, though, for someone new to guns, is to start with a quality .22LR revolver. Plenty of practice at a cheap price, and usable for HD, though not ideal, when you use the proper ammunition. A decent Smith & Wesson Kit Gun will set you back @$400, but you will have something your daughter will use to teach HER kids to shoot. New, that same gun will set you back @$700 - $800, so a good used gun might be the better way to go, not even considering that the older (pinned barrel) Smiths were better guns. Semi-auto .22s can be finicky as to ammo, and magazines have a habit of getting lost or damaged over the generations.
Good luck, and remember, you don't HAVE to buy anything at this gun show.