Ok you have a few options. Your AVR outputs 100W at 8 Ohms which is great because it's going to give you really fantastic sound with the speakers I'm going to suggest.
If your PC has HDMI out, I would highly suggest that you use the HDMI out to one of the HDMI inputs on the back of the AVR then run another HDMI cable out to your monitor/TV for display. This will use the AVR's built in D/A converter which will no doubt be better than the schiit fulla. You can keep the Fulla connected to your computer as a headphone amp and switch dynamically between them using the audio output selector in windows (right click the speaker icon in systray).
Speaker wise, these are a little pricy, but I'm going to suggest that you go out and get yourself four Kef Q100 speakers (they come in pairs at about $450 USD per pair) and a KEF Q200 center channel. I'd also suggest adding a subwoofer. The matching Kef subwoofer would be a good choice. At 100W these Q100s will give you a quite significant amount of very clean low end, so depending on your tastes, you may not even need a subwoofer. If you live in a condo or with a roommate, don't get the sub.
If you want to get the most out of your headphones, I suggest that you consider running RCA out from the AVR to a proper quality headphone amp like the entry level Schiit tube amp.
By the way, no doubt that your AVR supports 96KHZ sample rates for bluray playback, so you could run 48/88.2/96KHZ audio from your PC to it aswell.
Add a Blu Ray player to the system and run HDMI from the Bluray player into the AVR. You'll get full 96KHZ uncompressed audio in 5.1/7.1 channels and it'll sound great.
Take advantage of the AVR you have, and remember, speaker choice and especially speaker placement make a huge difference. You never put a speaker right up against the wall. Use (cheap) speaker stands so that the speaker drivers (the tweeter is inside the woofer on these) are at ear level to your seating position, which should be dead center and equidistant from each speaker.
By the way, once you get your whole shabang there setup, first, make sure you're on Win 10, as it, along with Server 2012 are the best sounding versions of windows for audio, and also, download JRiver Media Center. It's expensive, but the video and audio quality are spectacular. You can do so many tweaks to get the best sound out of your system it's ridiculous.
Edited by mistersprinkles - 9/19/15 at 7:55pm