If the drive is going to sit internally you can actually get a pretty good idea if it's going to fail via tracking the SMART status. With external drives it becomes more difficult as not all will tell you SMART status, especially if you buy you're own case. Western Digital's multi-drive systems come with software that tracks it.
Likewise, if you do a software RAID you can track the health of the RAID through your system.
So, basically, while you can't tell ahead of time if the drive is going to end up being a problem drive, you can usually get advanced warning of a failure. As long as you have more than one copy of those files you should be safe. One drive failure is actually relatively rare with good HDDs. Multi-drive failure is significantly more rare.
If you end up going RAID the only real concern you have is that if your house burns down, there's a massive power surge, or some other freak accident happens, all your data is in one place. I know a lot of people who promote the 3:2:1 method of backups which is three copies total, two local (original and backup) and one in the cloud or offsite.
Getting back to the original posters question, since you just need a single drive to do backup now (you can consider RAID systems later) I would recommend one of two routes:
1. Buy a LaCie external hard drive. I've had a number of drives from LaCie and never has one died on me. Western Digital and Seagate, yes, but never LaCie. the reason is they use Hitachi HDDs which are very good.
2. Buy a Samsung HDD and drop it in an enclosure. Which enclosure doesn't matter as long as it works the way you want. One nice thing about this option is you can eventually take that drive and use it in a RAID array.
If you do want to just dive in and start going RAID then I'm going to reiterate LaCie for a pre-built system for the same reasons I've already stated. If you want to go a more bespoke solution I recommend going with a Drobo. The reason I say Drobo and not one of the other, sometimes cheaper options, is because Drobos are very stable and borderline idiot-proof. You don't have to think about pairing drives, how you're going to repair the RAID if one drive dies, what you're going to do about expanding it... All you do is swap out the dead drive with a new one and it automatically repairs. For expansions, just slot in newer, larger hard drives. Also... Any size, any speed, no pairing necessary.
A Drobo will cost you about $400 to $800 for the case (depending on Drobo or Drobo S) plus another $100–300 depending on what hard drives you put in it. The nice thing about Drobos is you can start with just two HDDs and drop in more until it's filled as they're needed.
The one down-side of a Drobo is it's a software RAID in the box so it'll be slightly slower than a hardware RAID (though still faster than a single drive normally is) but unless you're using it for editing uncompressed video that's not going to be an issue.