If you don't go with a database, then you're likely looking at some sort of text file (JSON, XML, CSV, etc.) that you read into your app, modify, and write back to the file. This can become problematic If more than one user is trying to make changes to that file, which then requires you to do some sort of file locking -- which can be done, but frankly I'd rather let a DBMS handle that sort of thing. Also consider whether or not the data requirements may scale up at some point in the foreseeable future.
If in the end you still feel some sort of flat file solution is preferable, I'd personally probably go with a JSON format as easiest to work with in PHP. However, since I work with DB's every day that run from tables with 7 rows to 70,000,000 rows, I tend to think DB first and would tend to go that way with any data that will be used in a database-like way (inserts, updates, deletes, searches, sorts, etc.), since that's what they're made for, and will probably do it more efficiently than any file-based solution I cobble together.
PS: And don't forget about SQLite as a sort of in-between solution -- though closer to the DBMS side than the flat file side of things.