I've been happy over the years with
OWC Mercury Elite Pro from
Other World Computing (Macsales.com). I've owned several over nearly a 10 year period and have yet to have any of them die on me.
Since you're using Mac's, I'd recommend Time Machine (assuming you have one external drive per computer). If you're just using this as a method of sharing the data between computers, just leave it on the Mini 24/7 and have another external drive that functions as the Mini's Time Machine, and set it to also back up the music external drive. Then set up sharing in your Mac Mini to share the music files so that the laptop can access them.
But even this isn't enough for good protection. You'll also need an offsite backup. I use Crashplan for this purpose (Crashplan will do both local and offsite backups) but there are a number of companies that offer online backup services.
Having the offsite backups protects you against theft and fire, and the combination of local and offsite backups gives you the best protection that is reasonable for consumer-grade equipment.
Hope that helps.
Michael