For expanding disk space, an external hard drive is a good option.

For backing up hard drives, I would strongly urge using a portable external hard drive.

External hard drives are the same drives as used in the computer. In the computer it's pretty hard to shock or move the drive while it's spinning. In the smaller external case, it's incredibly easy to move a spinning (even just coasting) disk, producing "scabs" on the data service that can cause total drive failure.

Portable externals use the same drives as in laptops, with vigorous and secure "parking" and other "bump protections," and are much more likely to survive being (gently) "all shook up" inadvertently or intentionally. The portables are definitely a little slower than the "desktop" externals, and cost a little more; but for backups the cost and "performance hits" are usually of small concern.

Either kind should be treated like the last surviving egg from an otherwise extinct bird, packed in a box full of sharp hard objects, and should NEVER be moved while the disk is spinning - if you want your data (and the drive) to survive. The desktop kind should only be moved with greatest care and gentleness even when not spinning.

John