Any type of screen lid should be fine for your millipedes. They can't climb glass, but mine have crawled up the cord from their fountian and walked upside-down on the lid, so a lid is important.
As for substrate, millipedes need to stay moist, so whatever you choose make sure you mist them regularly. Personally, I use dirt with moss growing over it. If you use dirt you have to be careful of mold and always make sure you change their food before it gets moldy, because it will spread. If this is too much trouble, which a lot of people think, you can use leaves (make sure to wash them carefully) or unbleached paper towels.
As for mites, don't do anything. They help keep your millipedes clean. Also, I'm pretty sure I've seen mine eating the mites off themselves. Attempts to remove mites can hurt your millipedes, so it's really best to just leave them alone.
Good luck!