Villagers aren’t like animals as you can’t breed them, you can only give them the conditions and they breed themselves. The condutions being they need food and be in a village with not enough villagers.
I can’t remember all the villager mechanics but basically there are 6 villagers on farm land and one underneath with some doors. The villager underneath is a detector villager, it sees the doors and creates a village. The villagers on the farm land can’t see the doors so aren’t counted to the villages total number of villagers but are in the village. This tricks them in to constantly thinking they need to breed and will infinitely breed. The best bit, farmer villages will harvest and plant crops and pass them to other villagers meaning they always have food too. That is the simplest explanation I can think of but I’m there are videos by technical youtubers like gnembon or ilmango who explain all village and villager mechanics.
As for the different types, it is just random. There probably is odds of each one but I don’t know them and there is no way to control it. So it is just a case of letting them breed and killing all the ones we don’t need.
Villagers only have 2 or 3 trades unlocked but unlock more as you trade with them so always worth finding what all their trades are before giving them the chop.
What I envisage us ending up with is 2 or 3 farmers to trade crops with for emeralds. Maybe a couple tool smiths if we find any with decent tools for sale. Then a bunch of librarians selling various enchanted books.
A librarian selling mending books is the primary aim but getting the ither good enchants would be nice too.