What has worked for me...I use tupperwares as containers, the plastic grid stuff for yarn art works well as a poop screen when they are bigger. I put the lid on with one corner and a bit of wet tissue for humidity until they hatch. Keeping the tub upside down also helps the condensation run down the walls instead of onto the caterpillars. When I first hatched them I kept them next to the heat light on my snake cage. I put them in my dragon cage this time (it's really tall and has a shelf in it) and they are doing very well. It may take some creativity to find "just the right" place. Just sitting on my snake cage I get between 50-75%+ hatch rate, but cold snaps/drafts were a problem. I'm not so worried because all the eggs have been free. If I bought them I might try to be more consistent. I haven't used an incubator but they do grow faster when warm.
I hatch about 25-50 eggs at a time but usually only have one batch going. They take a about a month to get to where they want to pupate so if you want a constant supply of a certain size hatch them out based on how many you want to feed. I start to feed them when they are about 1" and offer pupae and moths too for as much variety as possible. You can slow them down by feeding them less but this will make for weaker moths if you want to breed from them.
I bought a buch of powdered chow and mix it up as I need it. I make it thin (still working on that) and pour it into cake decorating bags. It takes about 1 bag for 25-50 worms. It seems to stay fresh and is easy to dispense from the bag. I dispense about enough for 1 day. Extra just makes clean up harder. I'd feed fresh mulberry leaves and maybe learn to make chow if I had a tree, but alas I don't.
If you start from moths if they breed in the spring the first batch of eggs should all hatch. If they breed later or in the fall the eggs will enter diapause and you can keep them in the fridge. If you buy eggs, they are either diapaused or ready to hatch - the seller should say if you can store them or not.
Diapaused eggs - for me it's one to two weeks from taking them out of the fridge to hatch. Eatch patch is one females eggs.
Eggs and 1st instar. Babies need a bit of extra food so it stays moist enough to eat.
I don't want to move them too much when they are really tiny so I keep them on the lid and shake off poo each morning when I add food.
When they are big enough that poo starts to be a problem it's probably good to switch them over to the screen. When they are little it's easy to shake off. They will crawl under the screen and try and wander off if they run out of food. Otherwise they just park it and eat.
If they outgrow the tub any plastic tote will work. I used plastic shoe boxes with my first big batch. Once they are bigger I leave the lid mostly or completely off, they respirate too much and a lid is too humid.
When they are ready to pupate you can give them toilet paper rolls to spin cocoons in. They will wander off to pupate if they can and there isn't a spot they like. I've had a few get into snake cage or spin on the edge of the table. The cocoons harden and I cut them out and put them in a bigger tub. As they emerge they get right to work. I take joined pairs out and put them on an index card with a toilet paper roll on it. This keeps them contained and controls where the female will lay eggs - some are not so careful and make a huge mess.
Hope that helps! I think as long as you can find a spot that's warm enough they hatch, it's not as crazy work as the care sheets imply.