These are what I own listed in the order I use them. I'm pretty new to the DVD burning thing, so have a couple grains of salt:
Plextor PX712A fw 1.01: I love burning at 12x. Other than that, it's a solid but unremarkable drive--it does well with both + & -, and I can trust that the data's been burned right even at 8x & 12x. You have to feed it well, though--none of that aluminum foil frisbee garbage should go inside. Otherwise, get a less pricey burner.
NEC ND-2500A fw 1.06 (Herrie's): I think this is the best bang for the buck. It doesn't burn quite as cleanly as the Plextor, but it's trustworthy and not as picky with the media. If you install a DVD burner in your parents' machine, this should be it.
Lite-on 812s fw US0J: It runs Kprobe. Other than that, I'm pretty disappointed with it. I swear it won't open its tray if it sees a DVD-R in your hand. Kprobe scans sometimes look like roller coasters even burning slower than max. supported speed. I've really only used mediocre media cause I just don't trust the drive. Lite-on's been making dependable stuff for a while, and the drive seems solid mechanically... maybe it just needs some decent firmware.