I think most external hard drives are much the same these days...some may be a little quieter or a little faster or have special software to make backing up easier. Once installed they all work much the same way, the main choice is about the amount of space you want..usually the bigger the better.. a 1 TB can be bought for about £75ish.. Again depends what you want to do with it..
3.5" disk or 2.5" usually its just about the size of the box it comes in. Traditionally 3.5" disks were put in desktop machins and 2.5" in laptops.
External hard drives just plug into your usb 2 socket (some may use firewire for speed but not many). Once installed (some do it automatically others need to be installed with the supplied cd) they look like any other disk on you system in explorer and you can drag and drop just the same.