Well, first we need to clarify if this data is constant (unchanging) and the same for all users. If not, then we can forget about define()-ing constants.
If it is variable data, then we also need to know again if it is the same for all users or can be different. If it can be different, then we probably need to use sessions in some manner, though you still have the option of whether to save the session data in the file system (e.g. by the standard PHP session handling) or in the database (which can be done with a custom session handler).
If at this point it's still a choice between file-based sessions or database-based sessions, the filesystem approach is probably slightly faster, though if it uses the same database connection you were going to use already for that script, then the database need not be noticeably slower (assuming you've created a reasonably efficient database design). A database solution can, on the other hand, be somewhat more secure and robust, as it takes advantage of the strengths of the DBMS.