if you have the plex ios app you can use the remote functionality to control the plex client on your mini. Plex also supports the aluminum apple remote that comes with the apple TV or universal remotes like the logitech harmony series.
Another vote for remoter VNC. I've been using it since i setup my mini as a HTPC last year and its great. Less now that i've picked up a magic trackpad and the bar that holds the keyboard and trackpad together. Its very easy to use on the couch.
Screen Sharing is compatible with VNC. Enable VNC access in the Screen Sharing Preferences. (System Preferences > Sharing, select Screen Sharing from the list. The VNC option is found by clicking on Computer Settings.)
I found a gem of a client app for the iPad called Remoter VNC. When setting up the connection in the app, use your Mac account username for the VNC user, and the VNC password you setup in the Mac Screen Sharing Computer Settings.
Another vote for remoter VNC. I've been using it since i setup my mini as a HTPC last year and its great. Less now that i've picked up a magic trackpad and the bar that holds the keyboard and trackpad together. Its very easy to use on the couch.