Oh, this is exciting, Thorf! I hope you and your kids have a great time.
I think the suggestion about Mistamere nearby Threshold (from the 1984 red box) is a great one.
I had great fun starting a couple of friends out with that one, lasting about 3 to 4 years through high school. That specific adventure ended with chasing Bargle, him using the living statues disguised as him (as suggested in the box, I believe), and him escaping (of course). It was great.
You'll have to map out the 2 dungeon levels below the ruined mansion. I think you're boy would enjoy mapping those. I enjoyed making them up (and making them fairly interesting) as a new DM.
My second vote would probably be B1-9 for ease of use.
"The Lost Seneschal" from Tall Tales of the Wee Folk is a great scenario for someone more interesting in role-playing. Your daughter might enjoy the interactions in that adventure, since there is a little more role-playing (I can't remember if there might be some challenges, or riddles, that might be tough for a 7-year-old; but you could help her). I think it's a great fanciful adventure that captures a fairy-like woodland feel well. It would be a good starter one to throw in near the beginning of the adventures. There wouldn't be much mapping in it.
Thunder Rift is great for basic beginning adventures. I think Zanzer's Dungeon and continuing on through several TR adventures, culminating with being deposited in Bywater, Karameikos, at the end would work well. I have placed my Thunder Rift in the northwestern corner of Brun, near the Sylvan Realm, as there are supposed to be several human kingdoms nearby there.
I think B10 is a bit too broad and complex (it's a fairly long campaign) to start out with. But if you just keep it chopped up into scenarios that can be focused on, I'm sure it would be fine. I've never run it. The seige at the beginning is great, of course. It would probably take a few short sessions just to finish that part, depending on how you run it. Keeping young kids attention (or focused on a goal for more than 2 to 3 hours) would be a bit of a challenge, I'd think.
I think B11 and B12 are a little too broad. The first one involves an easy dungeon-crawl, and the map-making woulud be fun. I think B12 is too open of a sandbox adventure for new DMs and new players. And it's a "little" more grown-up, too, as I recall (as a previous poster said); I can't remember why. More violent encounters, maybe? Can't remember exactly. I was a little discouraged when I ran it many years ago and there was no map of the surrounding area around the castle in B12 when my players needed to scout out the landscape. I had to make up a lot of stuff. I think I had to figure out when there were patrols on the castle walls and stuff like that, so the players could figure out when to sneak in. I like the adventure plots and most of the encounters; there were just some loose ends to worry about, figure out on the spot, and/or prep for.
I agree with you that you will have to provide some NPCs to help. Most of the adventures suggested in this string need adequate parties of 4 or more. I'd suggest you play 2 NPCs -- 1 should be a new adventurer-type (fighter or dwarf, I'd think) that is experiencing the adventures along with the kids, and the second could be more of a patron-type of character, possibly 2nd level even, that kind of guides the characters along, and would act as a "pseudo-parent," kind of like a Gandalf figure. I think that would be helpful.
You could also run "The Dragon's Den" boxed set (part of the Challenger series that came out during the "Thunder Rift" era). I think that would be a fun introductory one. It can be used in the western area of Karameikos, as many people have suggested, since it's settlement and geographical locales were obviously meant to originally be in Karameikos. It definitely needs 4 (or more?) characters. The characters go up against dragons, but they have a bit of magical item help, too, in the scenarios.
Happy adventuring!