use a dvd writer as its best for backing up large amounts of data, in GBs. use a cdwriter if u have only about a few GBs. but i would advise u not to opt for external hard disks coz they will fill up with time and cost much more than a dvdwriter and dvd blank discs are very cheap too. dual layer discs are even better as they allow double saving.
Burn it to a cd or backup to an external drive. I use SyncBack to backup my data to another pc. You can download it from the link below. Scroll down and you will see it when you open the page.
External hard drives definitely are awesome. They can go up to 500 Gigs of storage for the really crazy models. If you have a DVD burner, you can fit quite a bit more data on DVD disks than on regular CDs (DVD=4.9 Gigs CDs=0.7 Gigs) so that is also a pretty solid backup method. DVD burners are actually pretty affordable these days too and are worth the investment.
Don't use a special disk. Buy extra hardware storage, so that if one drive crashes you will have a back-up. You can purchase one at Best Buy, or even Walmart. You don't want to use all of your storage space on downloads, you are simply enabling your computer to crash if you are using more than 90% of your space. Good luck!