I made some observations in my Plex storage future upgrade thread how I nearly filled 108 TB on my Synology 8-bay in less than a year doing Blu-ray rips from my collection.
You can start out with an external drive, but you may find yourself quickly filling that up. Commercial “consumer-grade” NAS are hideously expensive. If I didn’t buy my Synology as a gift for a family member who no longer requires it, I would’ve built my own NAS from the start. Between my tendency to over-spec everything, and gentle encouragement from other community members to over kill stuff as well (lol), tbh the cheapest way to do a media library where you have the physical discs is something like MergerFS + SnapRAID.
Do you have some older hardware you can repurpose in the meantime? You can try Open Media Vault, which is basically standard Debian with an easy to use GUI on top where you can easily configure MergerFS + SnapRAID. This probably will work out better than connecting an external drive in the long run.