I'm experienced with cats and kittens - and we recently went through this.
You don't need to train them, other than not to shred your furniture. With that, you just stop them, either clapping or you can spray with water, or a firm NO and get them down each time. Whatever works. We don't declaw ours.
So we have a cat tree that is covered with carpet and that's where our cat scratches and we also have a carpeted post that he uses. They have sisal ones but ours prefers the carpet ones. We got ours on Amazon and Costco. You can read the reviews - typically the ones with most reviews are better. The cat trees are a tad ugly and I wondered if I'd regret it - our cat loves it, we put it by window, he sleeps there and it provides exercise and scratching area. I recommend - get a neutral color like beige. Two cats can use.
We have found boys to be more loving/social in our experience. Just get neutered before spraying, etc. May be before they say need to. Ours started humping things.
We didn't need blankets for ours. We didn't need an enclosure. We didn't need book either - they are really simple. Just food (wet and dry for kittens), water (we have one of those fountain things - it's unnecessary, kind of a novelty item, and the thing I don't like about it is - it runs all the time, so drain on energy). A plain bowl of water is fine. Litter - we use clumping, and I did manage to find a cool litter box on Amazon where they jump in, so no litter gets messed around on floor.
We did the keep to one area for one day, then we found the cat was fine to explore. That's kind of extreme for 3 days - never heard of that. You live in an apartment - so there's no need to keep them in kitchen for that long. I think you should let them explore before then. Just keep it to gentle hands, and if kiddos have friends over, etc. just don't let them manhandle them etc. (kiddo friends can be a little over zealous, around here anyhow).
We did this - at night, we put ours in our laundry room - with the food, and litter and bed. We just had one of those little beds you can buy. That lasted about a month. We just didn't want the cat to wake us. Well, they cry. Now my sister did that forever with her two cats, for 15 years and it worked. If you want to start that habit early, it's a good one. Her cats would head to their laundry (or whatever room works for you) when they were tired at end of night. Kids were not disturbed during sleep. That's kind of an -enclosure.
You can put them in same room if you go out and don't want them getting into things as kittens. If you want, even when older as a cat (although they basically just sleep when older). Our cat - once about 6 months, stopped getting into stuff so we stopped putting him away when we were out.
Those would be my suggestions. Hope that helps :) Enjoy your kitties!