You'll want to look at capacity, data transfer rates and overall customer ratings on any drive, but it probably makes no real difference. Also consider USB flash memory and blank DVD media for backups.
Then again, you also want to determine if your computer issues are hardware or software related- if it's software(sounds like severe malware that's buried in deep) then you can format the drive and install fresh. However, if it's hardware- hard drive possibly failing, RAM going bad, motherboard going bad- you need to determine what the case is. Though if it's something severe like TDSS then you may need to use another PC to clean the drive because not even a basic format will help- TDSS buries in the rootkit and bootkit which normal antivirus and even formatting doesn't touch.
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Consider checking for malware before you plug in a second drive- a severe infection can jump to a second drive or flash memory storage when you plug it in. When I got hit with TDSS in 2010 I ended up infecting an SD card while doing data backup. It won't do you any good to infect a second hard drive.