These are just a list of classifiers that I know of, and is by no means all of them. This is more or less just a reference list for me, and I’ll probably be updating this as I learn more.
Trái: fruits (southern accent?)
Quyển: books and similar objects (northern accent)
Cuốn: books and similar objects (Southern accent)
Tờ: Paper or resembles paper
Chiếc: interchangeable with Cái (?) ((Northern accent))
Ổ: interchangeable with cái (?) ((Southern accent))
Tấm: big flat objects that are normally long
Miếng: for a piece of something
Ngôi: houses and similar buildings
Bức: flat objects with writing/pictures (+walls)
Bài: complete spoken or written work
Hạt: seeds, seed - like things, small particles
Viên: small round objects
Hòn: round, small objects + stand - alone islands & mountains
Khúc: part of a bigger object
Sợi: very long & thin object
Chuyến du lịch: holiday trip
Cơn: short term natural / phenomena
Trận: intense natural / social phenomena
Trận bão: storm (edit: Bão is usually used with Cơn instead of Trận)
Cuộc: events with multiple participants
Please correct my mistakes, and feel free to tell me some more classifiers!