The women's mikvah, of course. That's where most conversions happen, female or male. It's the nicest and usually also the cleanest. It's made for single-person use and is primarily used for taharat hamishpacha reasons. These mikvaot must meet strict halachic requirements, while the other kinds of mikvaot have different requirements, making them easier (cheaper) to create and maintain.
The keilim mikvah. This mikvah is much smaller and is used for toveling (also pronounced toiveling) your kitchen items. The halachot of this is too complicated for us to discuss here, but you can Google it if you are too impatient to wait. In Israel, the stores that sell kitchenware often have a keilim mikvah on site! How cool is that, right?! You will get your first real taste of the keilim mikvah when you convert, and then again when you get marriage gifts. It is a pain to schlep all that to the keilim mikvah (especially without a car), and you will have an intense fear of breaking at least one glass item. Note that a natural body of water can be a mikvah. However, you're unlikely to get naked and tovel yourself in it. Your new vegetable peeler though? That sounds like a great idea! (Remember to check with your rabbi about which bodies of water in your area can qualify as a kosher mikvah!)
The men's mikvah. This mikvah is the butt of many jokes. It's often not clean by female "ewww..." standards, and men generally do not get privacy. There can be as many men as can physically fit in that mikvah. Men's mikvahs are bigger than the women's mikvah, but have less preparation space. Think locker room. And that's how I usually compare the men's and women's mikvaot, like men and women's bathrooms. Thankfully, women's mikvahs are becoming more luxurious and spa-like every year. Mens mikvahs are beginning to be cleaner and less crowded, I'm told. Men's mikvahs are standard in many (most? all?) chassidic communities. Chassidic men use the mikvah much more often than other groups, often every week before Shabbat, and sometimes every morning. This is an area beyond my knowledge, I'm afraid.
Maybe your community doesn't have all these kinds of mikvaot. That's very likely. You may even have to drive a significant distance to reach any mikvah at all! (However, note that the mikvah is the very first "communal" thing that a Jewish community is required to build, before the synagogue or a school!)
In just about all communities, if you have a mikvah, it is a woman's mikvah. The men may use it periodically (especially before Yom Kippur), and the community also uses it as a keilim mikvah. (Note that they may alternatively use a body of water.) You probably have to make an appointment to use it.
If you have two mikvahs, my guess is that you have a women's mikvah and a keilim mikvah. A keilim mikvah can be much smaller and requires no preparation areas for people. It strikes me as significantly cheaper and, for most communities, more useful than a men's mikvah.
A men's mikvah is "easier" to make than a women's mikvah, but they're generally larger and do require some preparation space. My guess is that these are the least likely to be found in small communities, unless there is a significant chassidic community.