This is gonna be a bit longwinded, but I'll try to explain it as fully as I can.

The safest way to protect valuable data is on DVD/CD.
You can have an external hard drive fail, the master drive fail, the slave drive fail as well.
With DVD/CD's they're write once only, so nothing can delete, corrupt, or infect the data with viruses.
On dual-layer DVD's you can get 8.5 gigabytes of data on them, they only cost 25p each, so for £1 you've got 34 gigabytes of storage space.
That works out at £5 for170 gigabytes, for £10 you'll get 340 gigabytes, so I can't see the advantage of spending cash on an external hard disc.
If you choose to backup on DVD's, put them in jewel cases, and even if they do get minor scratches on them, you can buy a device for £10, that'll take the scratches out.
To do a full backup of your system is not needed, all you want to protect are your documents, pics, movies, and any other personal stuff.
If the data you're backing up exceeds the capacity of the DVD disc, when it's full, you'll be asked to insert another blank disc into the burner drive.
You can also write to the DVD in increments, as in mutisession, so you could backup on a weekly/monthly basis.

PS: a dual layer burner costs £20 at todays prices.