I think you'll like mice. They're sweet as little buttons and entertaining.
With keeping mice, first question is probably the most important. The cold.
Mice are best kept in temperatures between 65-80 degrees F. Of the two extremes, they are a bit more tolerant of cold than heat. A glass tank will hold temperatures at a more constant level than wire cages. If the temperature is expected to drop low, if it were me and I were determined to keep them, I'd avoid a wire cage which is prone to drafts, and provide a low temp source of heat in one corner that they can snuggle with or avoid as needed when they got too hot or too cold. I'd also be sure to get a reptile thermometer with a humidity gage to keep track of the cage temp and monitor it regularly. That way if the heat source caused the ambient temp to get too hot, I would know right away and act accordingly to adjust their temp. In fact, I'd get the set up going before I got mice so I could monitor it for a few days to get a feel for how it functioned with bedding, full water bottle and such before exposing my mice to a dangerous fluctuation before you got the kinks worked out.
Keep any wires and heat sources on the outside of the tank as mice are determined chewers. The under tank heater would seem like a good choice, but I'm not exactly sure how they work or what they look like, so I'll say as long as they have the ability to avoid the heat and cool down if it gets too extreme, like the heat source is only in one corner for example. You would only probably require the heat source if it's going to get extremely cold. Their body heat combined with bedding to burrow may even end up being enough to keep the temperature constant enough. But, like I said, get a thermometer and monitor the temp closely on a daily basis.
You'll want a wire mesh lid to keep them from escaping. It will also help make sure there's sufficient air circulation to keep the interior cage temp from rising above 80.
As for how many, it depends on the size of the tank and how well they ultimately get along. A 20 gallon tank is fine for about 3 mice.
Here's an excellent link to determine needed cage size, as well as other advice on sizing, floor space, and shelving:
I recommend females only. Males tend to be quite stinky. The urine from even just one is very pungent and can overwhelm a room. Many people cite odor as the number one reason they get rid of male pet mice, which is tragic.
Males also can only be kept singly as they are aggressively territorial and generally will fight to the death, even if they were originally raised together. There are exceptions to this, but they are in the minority.
With proper intros and proper space, females can be kept in colonies together. There's nothing sweeter than a little furry mouse ball of several snuggled together napping. Females also don't stink nearly as badly. As for keeping two versus three or more, it's just a matter of having a 'spare' in case something happens to one. If one dies and you had three, you still have two who are bonded with each other. So in the end, it's up to you what you want to do there. Keeping four isn't any worse or harder to me than keeping two.
As for getting mice and putting them together, it's important to do proper introductions.
The younger the mice, the easier the introductions. Since you already have hamsters, I would recommend quarantine (QT) no matter what. Preferably in a different air space than the one used by your hamster. Which means, not just a different room in the same house, but possibly a building separate from the house. If you're getting more than one from different sources, what I would do is keep them in QT cages and then introduce them to their main cage together at the same time.
To understand how to intro, it helps to understand what is important to mice.
Mice mark territory by urinating and smell is most important. The older they are, the more territorial they are to intruders.
So the cage they will live in together should be introduced to them at the same time so that it is completely neutral territory and neither can lay prior claim to it.
Making them smell like each other can help. This means you might try tricks like having them switch quarantine cages with each other for a couple of days before so that they get each other's smell on themselves, and they get used to the smell of the stranger before they actually face them. Another thing I've done is actually wipe the other mouse's soiled bedding all over each other before putting them in together. That way they further smell like each other.
Then I watch them closely for a few hours so I can monitor how they are getting along. There's going to be some chasing and squeaking likely as they work out a pecking order, but as long as there's no blood it should be fine. A good sign is if they snuggle with each other.
If they hurt each other, back off and go slower, even if it means keeping them in QT cages longer (though at this point the QT cages can be kept in the same house as the hamster).
If you don't have a separate QT location where you can keep them for a 5 weeks, do the best you can. While most people will tell you that you can't skip QT, to me it's a calculated risk. I know if I break separate air space QT then I am running the risk that any rodent in my house may come down with a nasty respiratory illness and die. I also know that having a reliable QT location can be darned difficult and sometimes you are just going to choose to skip it or at least minimize it.
If they come from the same store and same cage, they are pretty much already introduced to each other, so the careful intros won't be necessary. You'd still want QT for the sake of your hamster.
Hope this help!