I’m just trying to burn about five minutes of footage from FinalCut to DVD that needs to be playable on a standard player. Do I really need to go out and buy a program like DVD Studio Pro? Surely there’s a cheaper, quick way to do this.

iDVD. It's free and probably already on your Mac.

Yep, all you do is export your footage properly and then pop in a dvd and drag it over it and follow the directions.