Welcome to the forum

Not crazy at all, most people want what you want, and it's the default situation.

On each computer, save the files wherever you like, either to local folders or online OneDrive folders.

If you network the computers, don't share the folders in question. That's it.

If you're looking for greater privacy—eg other people use the same PC—then you could save your files only to a flash drive which you remove when you're finished.