The ones to look for are USB 3 external drives, and I would suggest either Seagate or Western Digital (the latter are very good, but a bit more expensive.) I have a basic Seagate 1TB drive, which I got for around £60, I think. Some drives have lots of 'features' , eg backup/ NAS/wireless. but you pay more for these, and they are not always as useful as they sound. Go for a good basic drive. If it is a 'Green' drive, it usually means it's slower. Get a 7200 RPM one.
Just to add - don't get a portable one if you want to do a full system backup, as not all of these will allow this. Better a desktop External HDD for this.