The standard Plex app gives you a ton more than just streaming your own content. You can easily share the media with friends and family, access online channels such TED, Revision3 and TWiT plus lets you queue up online videos from Vimeo and YouTube to watch later.
While the media server and the app on your device is one powerful combination, a Plex Pass subscription is easily the best way to go. With 3 different options, Monthly for $3.99, Yearly for $29.99 or a Lifetime for $74.99. The Plex Pass subscription takes the Plex for Android app out of the equation and offers you the Plex Pass app for free. With Plex Pass you gain Chromecast support (which will come to the regular PLex for Android app at a later date), Plex Sync, CloudSync, Early access to new features and multi-user control. Plus a whole lot more.
If you are undecided on what you want to do, that is ok. Pick up the Plex for Android app while it is half off, install the media server and give it a run for a little while. I personally have a lifetime Plex Pass subscription and have the app on my Google TV box, both tablets and my phone. I use it daily and it is one of the reasons I was able to cut the cord on cable so many years ago.