For a long time, I used a Raspberry Pi running stock standard Raspbian with an external USB drive connected. I just Googled around how to set up a Samba file share, and that's all I used. Didn't really see the value in any media-specific software, myself. For me that was secondary to the LAMP stack web server, anyway.
Biggest thing I would recommend is making sure you have, from day one, a full backup of your data and any configuration necessary to read the data.
If you're thinking about wanting access away from your home network, my recommendation would be to do it by also setting up a VPN and connecting to your local network, rather than something that is directly exposed to the Internet. That is, unless you want to be able to share files with other people at ease.