I bred mice, also had lots of mice, so here's my tips for you. :]
1. Bin cages are easier to find, bigger and cheaper than any "pet cage" from a store, easier to clean, and less likely to break (compared to a cage that can rust, a fish tank that can crack, or any other type of cage). Watch out for any extra edges along the bottom of the bin, some bins have "feet" on the bottom but that means the plastic comes up and mice WILL chew that. Have metal mesh on hand for repairs if you need to.
2. Almost every bottle seems to leak. Glass ones don't usually work, but go for the best quality water bottle you can.
3.
Chewy.com has the cheapest rodent food I've ever seen. Mice need a block diet, with other things as very rare treats. My mice liked cooked rice, unsweetened cheerios, and occasionally plain meat with no seasoning or oils on it.
4. DO NOT get males in the same cage. Nine times out of ten they will fight. Same logic as betta fish... sort of. However, pairs or trios of females would be perfect! They will snuggle together at night, groom each other, fight for the best snacks and generally be great friends for each other.
5. Places to look for toys. Keep in mind fabrics will be hard to clean, and plastics might get chewed. Dollar store "storage" container, bird toys, baby toys that are plastic or look fun to climb around, cardboard, cleaned out plastic food containers, packing paper or paper with non-toxic ink on it, and branches are all great toys.
6. Get a flying saucer instead of the standard wheel if you plan to do so. The wired wheels can get their tails caught and rust or are harder to clean. The saucers aren't nearly as bad.
7. When picking out mice, I've always had better luck going to a reptile specific shop and buying feeders. Generally MUCH healthier, but they won't always give you females. If they won't, look for mice that aren't hunched over, don't sniffle or shake, have a plump healthy looking body and aren't goopy around the eyes or nose.
As for names, I had several lines of mice going with each generation or line getting a theme. I used spices, cheeses, breads, coffee drinks, and types of cows for my various lines. :]