1) RAID is not a backup. If you want to protect yourself against data loss, you want a backup, not RAID. Conversely, even if you have RAID, you still need a backup.
2) RAID is for redundancy (except for the misnamed RAID 0, which is not redundant despite the R in RAID standing for Redundant). If you want your system to continue chugging along without downtime despite the failure of a drive, you want RAID.
3) Hardware RAID is just a computer on a board doing the RAID parity calculations. It made sense back in the 1980s when these parity calculations could eat up 60% of a CPU's processing cycles. It makes very little sense today when it takes up less than 1% of a CPU's processing cycles. Just have the PC's CPU perform the RAID calculations (software RAID). About the only reason to use hardware RAID nowadays is if you want the storage system to be robust against software corruption or hacking. So basically, if you aren't a government TLA organization, or a megacorporation trying to protect sensitive and essential data, don't bother with hardware RAID.
4) It sounds like your music collection can fit in 3 TB. That is not huge. If it can fit on a single drive, it's not huge. Single-drive backups are the cheapest and easiest form of redundancy. The other reason for RAID existing is for when you have data sets too large to fit on a single drive (I backup my NAS to a RAID enclosure with 4 drives configured as 12 TB).
Based on your description (desire a local backup), just get a large external HDD and backup your files to it. Since you already have off-site backups, you can keep it at home. External because the "offline" requirement still applies. There's little point having a local backup if whatever corrupts the computer's HDDs also corrupts the local backup. Plug it in once a month or once a week to make an incremental backup, unplug it, and put it in a drawer.