Option #1 - If your phone's supported microSD size is ok for you, you could install the android Plex client, sync what you want to take with you, and output via Miracast to a TV or your phone might support a type of cable from your phone to the TV:
https://www.howtogeek.com/201822/how-to-connect-your-android-phone-to-your-tv/
Option #2 - If you want more storage, you could buy a cheap android box+external HD, install the android Plex client, sync what you want to take with you, and output via HDMI.
Warning...Plex syncing is a little fiddly. Sometimes the options take a little digging to get to. You might consider Kodi (might check compatibility with your phone/android box depending on which method you choose) instead of Plex for a portable option. I have Plex Pass, so the remote/syncing works for me...unsure how well it works if you don't have Plex Pass.