Just my 2 cents here but I am not a fan of external drives at all. It just seems to many folks have problems with the enclosures and interfaces. So I cannot really recommend one. But I do have a suggestion. Consider backing up to the cloud. Or just buy another hard drive (or SSD), temporarily install that as a secondary drive in this computer, backup your files to it, then remove the drive before you sell the PC.
Beyond that, you really need to state how much space you need, and your budget.