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Congrats Duncan! Baby Fat Tails are so cute.
I raise babies in small rubbermaids (with several 1/8" holes drilled for ventalation) with paper towel as a substrate. I mist down the paper towel pretty well when I put it in initially and after each cleaning. In between times I lightly mist as I see fit. I've found humidity to be much more important for babies. Keep an eye on the toes to be sure the tips are all shedding properly.
For a water dish, the easiest thing I've found is the little plastic flower pot dishes (guessing at 3"-4" in diameter). These are shallow enough that the little guys can get in and out easily but will also hold enough water that it shouldn't evaporate daily. You can use the same dishes turned upside down for a hide and cut a little notch out for a doorway.
Typically, babies begin feeding three to seven days after hatching. They usually have enough energy from absorbing their yolk sac to go for a couple days at least, so don't worry too much if they don't eat at first. Be sure to remove any uneaten crickets though. I usually feed in the evening, and if there is anything left in the morning I remove them.
I offer 3/8" size crickets and keep track of how many I put in each cage for the first few feedings just to be sure they are eating well. After they are eating good, I try to stay on an every second day feeding schedule with them.
This is what has worked for me and I hope some of it will help answer some of you questions