I don't personally get why people buy external headphone amps for the FiiO X3 when it comes with a decent built in headphone amp. You should try it by itself first. If you are really convinced now you need better than the X3, then get the X5 with it's better hardware
I haven't heard complaints about the Audio-GD equipment needing returning. The best desktop dacs/amps are going to be better than the portable FiiO stuff because they can provide more power. So if you want the best sound quality for your money to get the most out of your DT880s, you can do much better than the FiiO with the budget you have indicated by your options above.
Also, most head-fiers consider gaming headsets to provide pretty crappy sound for the money. You might find that using a Xonar DG soundcard for its Dolby Headphone feature to sound pretty good with your DT880s. It's a different headphone experience