bitcoin core from Ubuntu app center. Most instructionals I've found run things from Terminal though.
Discussion
This is the way. It'll want to use sone directory on your root system by default; you need to make sure the directory its using actually lives on the external disk, either by mounting, or setting bitcoin core to look somewhere else than the default. Depends on your OS.
Linux.
Either way will work. In bitcoin.conf you can set the data-dir to /mnt/external or wherever you have your ssd mounted.
Here's a neat tool to help guide you: