Compared to Arch(-based): Accesing the latest packages. It’s not impossible, especially if you go for Debian testing repos, but it’s definitely extra work.
Compared to special-purpose distros (i.e. gaming, portable, high security/privacy, pen-testing): Whatever their special purpose is will usually be harder to achieve.
Compared to huge corpo distros (SUSE/Fedora and derivatives): Ease of more intricate setups and maybe some security testing.
Compared to Ubuntu: Paying a corporation to not withhold security patches from you.
Second this. What you need for high quality media is space, not speed. For any single stream, network and drive will be fast enough anyway. Your typical HDD offers like 4-6 times the bandwidth that a regular Blu-ray can provide. You can get 8TB HDDs for the price of 2TB SSDs. Random access doesn’t matter for that application.
You might want to invest in redundancy and use a RAID 1 or RAID 10 array, depends on how valuable that media is to you or how long it would take to recover in case it’s lost. A simple solution would be a btrfs software RAID, in case your are after something like a Linux home media server with Jellyfin.