I'm not sure a new computer 'just for additional storage space' is the right way.
You say you have begun video editing so are either or both your current computers up to the task? Does one of them, or do they both, perform as you wish?
If the answer is yes, then I would say that you just need additional storage, not a new computer. But don't let me deny computer manufacturers added revenue by discouraging you from buying a new computer!
If you agree and decide to go for additional storage only, then that should be an external hard drive. Internal is fine but connecting it can be a bit of a problem if you have never done it before. There are pitfalls. With external storage it is as easy as plugging it in to a USB port, and it would serve both computers.
Just one thing you may not have thought of. Backup. We have a saying here. Backup Backup Backup. That's 3 copies of the original file. For that you need 3 different media, and in this case I mean 3 different external drives.
Why? If you are saving hundreds of MBs of videos and something happens, eg computer failure, power outage, external drive failure, malware infection, etc, then your original is all you have. If you lose that, you lose everything. But we go further. If you have just one backup and lose the original, then you no longer have a backup. It has suddenly become an original. That's why we say multiple backups, 3 of them.
Also, backups must be on separate media. We have seen users who backed up to a different partition on the same drive then wondered where it went when the drive failed.
What I am saying is, with video editing and the large files it produces, more than one additional storage device is needed. But it is also true with all personal files.
I have two computers, both with 250 GB HDs. i've begun video editing and i am bumping up to both HD limits. seems to me i can buy one new computer with a much larger HD or is it possible a new external HD would serve both computers? thanks.