I'm looking into purchasing a off the shelf brand hard drive for my backups. Which brand and model do you use or recommend? BTW, not interested in going the enclosure/bare drive route for my backups unless that's highly recommended.

 I picked up one of these from ebay USB 2.0 TO SATA S-ATA 2.5 3.5 IDE HD HDD Hard Drive Adapter Converter Cable  And use any old hard drive I find laying around or I can find cheap.
 
If you're looking for an internal secondary drive, I've always relied on the black Western Digital Caviar drives.
 
 One thing to consider, if the drive you are installing is intended to be pluged in at all times, there is a slight chance that something could happen that would result in loosing both drives therefore no back-up.
Blue-Ray burners are pretty cheap on ebay, you can burn about 25 GB on a normal and about 50GB on a duel layer disk. IMO nothing is more secure than a hard copy of mission critical data. JMO 

For backup purposes, the brand/model is much less critical.
 
For long-term convenience, you might consider an eSATA docking station.
Slide in a bare SATA HD (just like a RAM stick)... and you have an eSATA HD.
Super easy to swap drives... and relatively inexpensive.