A few good examples are listed below but the basics are that the cage must be:
Well Ventilated - Rodents require good air flow to prevent ammonia from their urine building up
Escape Proof - Mice can squeeze through some very small spaces, and can easily escape
Easy to Clean - Mice cannot be potty trained like larger rodents can. Every surface of whatever cage style you pick will need to be cleaned at least once a week to reduce smells.
Big Enough for the Number of Mice - The minimum size for a trio mouse is a 10 gallon tank or equivalent, and for a single male it is a 5 gallon tank or equivalent. I would personally go a size up (so a 10 gallon for a male and a 20L for a trio of females) if I were keeping mice as pets. Bigger is better...if you can afford to fill it with the bedding, hides, and enrichment that the mice need to feel safe.
Pros:
Sturdy
Mice are easily visible
Generally easy to clean
Often available used for cheap (be sure to sanitize these before use)
Cons:
Require you to purchase a metal mesh lid, or make your own (The mesh lid can be almost as expensive as the glass tank)
Require you to purchase a metal water bottle hanger (unless you DIY a water bottle hanger)
Heavy, especially if you are lifting them onto higher shelves
Pros:
Affordable
Lightweight and generally easy to clean
You can easily make a larger enclosure for your mice than is available commercially and
Online guides are easy to find
Perfect if you like to DIY
Cons:
Require tools, and some materials can be expensive (i.e. 1/4" hardware cloth)
Can be time consuming to make
Lightweight, more easily bumped or knocked over
Mice will chew at the inside of the plastic and on whatever you use to secure the hardware cloth or metal components to said plastic
Pros:
These are available in every pet store that sells pet hamsters. No wait, that's a con for both the mice and the hamsters.
Cons:
None of the plastic and wire pet style cages are appropriate for mice. Mice can get their feet stuck in the wires or get stuck in the tubes. The wheels included are too small for fancy mice. The interior space is usually too small.
These are available in every pet store that sells pet hamsters.
Pros:
Are frequently large, and available easily from large retailers.
Cons:
These seem like they would be easily chewed through. We have no personal experience with these cages, but if there is exposed wood then the mice will eventually chew out of the cage.
Bare wood will quickly become saturated with urine.
Please reach out if you have had any personal long term experience with these cages, good or bad.
The AFRMA has a series on housing mice and rats that starts here: https://www.afrma.org/house4mousep1.htm (Please note that prices have changed since that website was created.)
Reddit's r/PetMice group has some good housing guidelines.
The Frosted Cookie Mousery has a good Mouse Care page, with several examples of good housing.
The Finnish Mouse Club has an extensive Care Page here.