I just use first and last name when buying a ticket, although my passport in includes my middle name. Since there is no space provided to enter your middle name when buying a ticket, you can put both first and middle (as much as will fit) in the space for first name but some strange conflation will show up on your boarding pass. Ima Popcorn Kettle will come out Imapop Kettle, for example. Unless your middle name is short, better to stick with first and last or use the middle initial.