There are many apps that let you stream media from your PC (assuming that you've set Windows to share your PC's media library on the network via DLNA). For example, the free app
MediaMonkey (which I like a lot) or the free app
Wondershare can stream both audio & video files from a PC. Or if you want a full-featured "cord-cutter" TV experience, you could install the free, open-source app,
Kodi which can stream music & video from your PC (and do things like stream live broadcast-TV & movies).
As long as your router is powerful enough to handle the traffic for whatever it is you plan to stream (e.g. HD movies) from your PC, then your nVidia Shield should be plenty powerful enough to decode it. (So there should be no need to run a media server like Plex on your PC, which reduces the video quality.)
As a side note... If you go with Kodi, there are several remote-control apps, like
Kore or
Yatse that let your phone remote-control Kodi. If you go with MediaMonkey you may be interested to know that there is also a free
MediaMonkey media player for Windows which is great for playing and managing your music & videos on your PC (making playlists, editing tags, etc.). It can sync to MediaMonkey for Android via USB or WiFi. The free Android app,
MMRemote, can remotely control MediaMonkey for Windows.