I presume you would only have the external hard drive operative for backup purposes, say weekly, and therefore its use would be small compared to the PC. In this case most hard drives of about 250GB size or above would suit your purpose and provide plenty of room for backups of photos, videos, documents and of course your operating system plus programs installed to it.
I use an Icy Box with a 320GB Maxtor drive, my son uses the same enclosure with a 250GB Western Digital and my daughter uses a 250GB Iomega. All have proved satisfactory. If you wish to buy a ready assembled external hard drive there are many on the market; for example PC world sells these click here which cover a whole range of sizes and manufacturers.
As for a refund for lost documents or other data, I know of no manufacturer that will provide this as no manufacturer is in a position to know exactly what you may lose at any given time.
For backup software I use Acronis True Image which I find simple and very user friendly. I believe most others that use it would tell you much the same. Certainly it provides a simple user interface and walks you through the backup process with excellent help files if you need them. In the unlikely event of a catastrophic failure in your PC`s hard drive, re-installation is as simple as the backup process.
Hope this helps.