It looks like your amp has a DAC built in. It doesn't have any direct PC interface, so you couple of good options:
1) Use an external DAC to connect to AUX. A quality DAC should deliver better quality than connecting to the built-in sound on your PC.
2) Get an adapter to convert the USB from your PC to Coaxial or Optical. Audio quality would depend on the quality of the adapter and the DAC built into the amplifier.
Background information:
The audio out on your PC is a basic DAC. The problem is that the inside of your PC tends to be an electrically noisy environment, and depending on your machine, audio quality was likely not a primary design goal.
External DACs provide better noise isolation, and often have better components than what came with your computer. They can be under $100 to over $100,000. If you choose to buy a DAC, pick a budget and then look at reviews. There are many designs out there each with a set of fans and detractors. Listen to them in person if you have the option.
Upgrading:
The right upgrade can depend on what you are noticing about your system and what you want to achieve. For example, what kind of music do you want to listen to? Do you want fine detail, rich sound, etc. Adding a DAC (Schiit Bifrost 2) to my system added improved detail and eliminated the thin, fake sound that my headphone jack was producing. The first question is what does my system not do that I would like it to do? If you want less noise, better detail, or a more full sound, a DAC upgrade may be a good option for you.
Headphones:
Since I don't have your configuration, I would recommend taking a good listen to your equipment and seeing if it sounds good to you. I recently set up a system about 4x more powerful and found that to be adequate, but your mileage may vary. One nice thing about your amp is that it does have a preamp out that you could connect a dedicated headphone amplifier with whatever power you desire.
In summary, you could just get an adapter to use the amp's built-in DAC with coaxial and optionally add a headphone amplifier to get a bit more power on the headphones and be a very happy camper. If you want to go higher end, the sky is the limit.
