Don't confuse storage space (drive capacity, 256GB) with memory. They are two different and unrelated things.
If the storage of your computer is running low because you have too much stuff saved on the drive, the fix is to do as you plan and get that external hard drive. A drive that becomes too full will cause the Mac to stop booting. Ideally you want to always have a minimum of 10%-15% of the startup drive capacity free.
You'll have to decide what stuff you absolutely need/want to keep on the computer's internal drive and what stuff you can store externally. Anything you have saved in your Home folder, including things in the Documents, Downloads, Music & Pictures folders, can safely be kept on the external drive.
The stuff that takes up the most space on the drive is videos, music and pictures and downloaded items. All of those can be stored on an ext drive. Move these things to the external drive and then delete them from the internal to free up that space.
Don't concern yourself with anything outside of your Home folder. There's nothing there but stuff required by System to run the computer.
Importantly, if you aren't doing so already, you should use another external drive and back up your files with the Time Machine application. A simple fact of computing is that if you don't have data backups, then you will lose something. The Time Machine app is already installed on your Mac.