Hi - glad you're coming to Summit County! I just noticed again your earlier posts from the start of this year, so obviously you've been planning this out for a while. Nice to have visitors who are carefully looking into their options and thinking about what will help them enjoy their visit most.
I teach beginners at Breck, so I know more about our learning terrain than I do Keystone, and I might be a bit biased
However we're all one big happy corporate family
so I'm happy wherever you go. (But I'd love for you to come visit at Breck!)
One big difference - the major beginner learning area at Keystone is at the top of the mountain! That's because you can take the gondola from River Run up to it, and down from it. Takes a bit longer to get there than being right at the base, but also is kind of neat because new skiers are getting to go up to one of the peaks for that "mountain experience" even without having to know how to ski down from there. I think there might be some base-area beginner area too (perhaps at the Mountain House base?) but I'll leave that to one of our many Keystone regulars to clarify.
At Breck, we've got three bases for first-time learners: the Beaver Run base area at Peak 9 (where I teach), the Village base area at Peak 9, and the Peak 8 base area. I do think we have great learning terrain over at Peak 9. A good mix of protected, flat "learn to move on skis" yards, some gentle learning areas to climb-and-slide, beginner surface lifts, and a 6-person high-speed lift specifically over our easiest green "real runs" once somebody has learned basic sliding and stopping skills. Typically we'd have you out on those runs by the afternoon of your first day, though of course, the lessons are always fine-tuned to the needs and wants of the guest. We have similar stuff over at Peak 8 but I think either Peak 9 base is a bit better for never-evers.
The staff is great at all the locations - Keystone, Breck 9BR, 9 Village, and 8. I do see quite a few folks who take a lesson one day at Keystone and another day with us at Breck or vice-versa, so take advantage of the various locations you can ski with those multi-day passes.
I will say this - if you're staying at Keystone, getting the family out to lessons at Keystone is a heck of a lot more convenient than coming down to see us at Breck! I do think that for the first day or two, you'd be best off taking lessons at Keystone just from the convenience factor. Breck is a good half-hour drive from Keystone or longer on the county's free bus system, so for your first day - hit the hill you're staying at. Since your husband already skis, he might enjoy checking out the Basin one of the days you're taking lessons at Keystone. Then maybe you all come down and check out Breck on one of the days.
A-Basin is a great mountain, but it's not primarily known as a never-ever learning area. I think the actual Vail Resorts-owned properties of Keystone and Breck (we have a marketing agreement with them and some past-ownership commonality, which explains why your multi-day ticket is good at the Basin) ski schools might have more of a focus on having strong never-ever programs.
Private lessons are usually optimal but do cost a whole lot more. Our group lessons are quite good for getting never-evers turned into skiers enjoying sliding down a "real" green run from the top of a lift, in relatively short order. Also, the kids might prefer to be learning in a group of their own age the first time, while you might enjoy not having to be responsible for them at all while you're learning.
Group lessons the first day and maybe the next, followed by a "Family private" might be a good lesson strategy. I think you'd get more benefit out of the private lesson once you and the kids had all gotten the first-time basics out of the way. And by then, you might all enjoy showing each other what you've learned and learning together.
Enjoy the trip - Summit County is a great place - and make sure to get out to the restaurants, live theatre, workout studios, shops, and other fun stuff in our towns here too!