An extra internal hard drive would be the fastest solution, but installation requires some technical know-how.
After the first full backup, which could take two or more days to complete, things go faster, but if you create a lot of music, video, or image files each day, you should consider a faster solution. Online storage services sound great until you realize how slow they are. If you need to take your backup with you, you'll want a drive that's small enough to carry around. You'll save relatively little by buying less capacity than that so get as large a drive as you can afford-at least as much capacity as your computer's internal hard drive. You could spend $100 to $200 on a 2 terabyte drive, or closer to $300 for a 4TB model, but do you really need that much space? A 500GB to 750GB drive might accommodate your needs well into the future.