Thanks for all the feedback and suggestions, everyone. I thought I'd provide an update on how I've decided to proceed.
For now, I've decided to start small, and focus on having a local library on my laptop. While having the library available on my server in case I need a book while I'm not at home sounds like a great idea, in practice, its probably not something that will be used very often, and certainly is a 'nice to have' rather than a 'need to have'.
I've started with a duplicate copy of the library from the server, and have started to clean it up using calibre running locally on my laptop against a local copy of the server. I have FreeFileSync running on my laptop to back the local database up to a NAS I have.
My plan is to take the existing library of just under 3000 books that I've inherited, and clean up the metadata, get rid of duplicates, etc. Once I have the library in a shape that I'm happy with, I'll revisit trying to make the library visible on the internet either using a second copy of calibre on the server, or by using calibre2opds.
Thanks to everyone for your advice and suggestions!

Brawny