The role of the Media Server is to provide access to your entire media collection.
Be it local access while at home or also remote access while not at home.
There are at least three different options that you can choose:
JellyFin is a fully open-source and totally free media server solution that is growing a lot in the recent years. Its pretty stable and its my top choice for these reasons. The mobile clients might not be top notch, bit they get the job done. My installation instructions are here.
Plex is widely used. Its proprietary software and you need to pay for using it. People says it's very good but the UI feels a bit old. Also has a pretty good range of mobile apps and speciale mention, allows you to stream tour contents while outside home via Plex servers, which could ne tour easiest way for remote access. I didn't like it for the same reasons.
Emby used to be open source software, its now closed-source and pay for access at least advances features. For these reasons I didn't choose it.