There is NO Right answer to where "YOU" Store the LR catalog and the actual images files.
Both can be stored anywhere you like. As for the catalog it has to be stored on a drive that is physically connected to the computer you are running LR on. For the image files they can be stored locally, on a drive physically connect to the computer or on a drive connected to your LAN (Local Area Network).
I personally don't use my notebook for anything else than to store the images I take when traveling. I do import them into LR on my NB but I don't do any real editing of them on the NB and when I return home I Copy them from the NB to my DT system and then import them into my Main LR Catalog file.
Others do do editing on travel systems and then Export as a Catalog, including all the image files, and then Import From a Catalog when they get back to their main system.
The right way is the way it works best for "YOU".
If ruling out placing your catalog of the external disk alongside your photos then consider using Dropbox method described at this linked page Syncing And Backing Up Your Lightroom Catalog With Dropbox
Regarding syncing presets, this was also possible via Dropbox until Lr7.3 when Adobe changed the location in which presets are stored. Lots of folk still trying establish an alternative but I've not come across any who have succeeded.
Thank you both for the tips. The Dropbox sync might be what I'm looking for (I think I might get it working with OneDrive), I just need to reduce my Catalogue size from 5GBs.