I’d probably go with a Synology or Western Digital plug and play NAS.
Before you get a bunch of “raid is not a backup” comments, it’s important to understand a NAS isn’t really made to be a backup of itself, although it’s possible to set it up as just a bunch of drives (JBOD) and have them clone each other.
It will cost a good amount of money to get a NAS that can transcode. If everything’s direct play you can probably get away with it, but for a noob I’d recommend getting an Nvidia shield for a Plex server, and just mounting the NAS to the shield.
Both WD and Synology have the ability to access your data from anywhere through an app or website. There are a dozen other ways to do this, but a prebuilt plug and play NAS will be the easiest.
TL;DR: for the smoothest experience, but an off the shelf NAS. It won’t be the cheapest but it’s the easiest for a novice.