Except for the pull-over style (a back zip, or collar fastening), the jacket should fasten on the non-sword arm side, that is, zipped on the left for a right-handed fencer. This is to prevent a blade penetrating through the opening. The jacket must not have any holes for the same reason.
Jackets come in different weights (measured in Newtons of force) offering levels of protection. 800N is the current minimum for club use. When buying new, get an 800N jacket.