Ok first of all disregard any advice to connect a permanent drive with USB. It will suck. You will get disconnects and maybe even filesystem failures. And yes you can recover from failures (most of the time) but why polish a turd?

If you can add an internal hdd to the NUC that's all you need. Get one in whatever size you need and you're good to go.

If you want to safeguard against that HDD crapping itself then you can use a secondary HDD on USB. Connecting a HDD occasionally to USB for backups is ok. Keeping it connected 24/7 isn't. Use a specialized backup software like Borg Backup, take a backup of whatever you consider essential data, and keep the backup HDD in the drawer the rest of the time.

You don't have to get an external HDD btw, you get a crappy USB enclosure and a crappy HDD with a shiny brand on it. Get a regular HDD from a good brand, it can also be a 2.5" (laptop) HDD, and an USB SATA adapter. Also, Orico makes some nice HDD cases for drawer storage.

If a second HDD is too expensive for you get an optical unit (can be USB, can be internal + USB-SATA adapter) and burn backups to Blu Ray discs from Verbatim with parity data created with par2. Store the written discs in zip-up CD wallets or jewel cases, not in bulk spindles. You can also burn DVDs if BRs are too expensive where you live. DVDs can also be long-lived if stored properly and any backup is better than no backup. But BR are really best for durability.

Don't listen to advice about making RAID this and RAID that. How much space do you need? They make 20TB HDDs nowadays. Get one HDD and be done with it. Do you want to spend 5x more and also have to buy a NAS to store them, and learn about RAID levels and in how many ways they can fail? Do you need 100 TB? Do yourself a favor and get one single drive and take periodical backups and you'll be golden.