It sounds like you are off to a good start. Your bedding is fine. I would not use peat just because I don't see the point of paying for bedding to raise worms when bedding can be obtained for free.

You understand, of course, that the cardboard box won't last very long. You will want to get your plastic bin ready soon.

I would stick with paper- newspaper or corrugated cardboard. Worms dont'like a high acid environment and peat is acidic. You could sprinkle a little ground limestone the peat to adjust the ph a little.
I always give the worms some food. They need to eat. Just don't overdo it. Base the amount of food scraps on how many pounds of worm you have.
Good luck

Uh, oh. I have already messed up. :( I read that the worms will die if the bedding is too acidic. I have organic garden lime in pellets -- can I ground that up and sprinkle on the bedding?

The problem with acidity is, IMHO, overstated. Are your worms abandoning the bin en masse? If not, then your bins are not too acidic. The process of organic matter breaking down will balance the PH. Unless you are feeding a lot of very acid food, I doubt PH is a problem in your bin.

I read somewhere that bedding that is too acidic could kill worms. I did notice that a good bit of my worms are now not moving -- I figure they must be dead? Do worms sleep? Are some lazier than others? I wasn't sure if the acidity was a problem, so I mixed in some garden lime. The instruction sheet that came with the worms said that canadian peat moss, cow manure and shredded paper are good bedding material, so I emailed the farm to ask if I am doing anything incorrectly.