from my "introvert" experience a good way to make new friend is by bonding over a mutual experience.
In school it's easy because you're both at the same school and such. Out of school best way is mutual interests you can do together (videogame, sports,...).
A good way would be to join a club with a good amount of member, you'll be able to talk with a lot of people and single out at least one or two you like. Try to start hanging out with them outside the club after enough time to know them better. Like just grabbing beer together, meeting some of their friends and such.
As for the slightly broken people, in my experience as long as it's not displeasing or awkward being around you, there's no problem to be had.
