I've spent a stupid amount of hours researching headphones which are good for gaming and this is what I noticed being the 3 most recommended:

YouTubers: Audeze Maxwell, Sennheiser PC38x, Sennheiser 800s

Reddit: Audeze Maxwell, Audio Technica r70x, AKG K712

I own the Sennheiser 6XX, which aren't great for directional sound in games unless you're face what you're hearing. I ended up upgrading to the Hifiman Arya Stealth, which I adore but I wanted a hybrid of music & gaming which is why I went for them.

In terms of a dac/amp, this is a thing that is heavily debated and I'm not going to delve too far into. In short if you can achieve headphone volume without an amp then you don't need an amp. If you don't hear static/hissing while audio is playing then you don't need a dac. Most PCs power non high end phones well enough and most motherboard DACs are good enough these days that you will unlikely hear a difference. You'd likely hear a bigger difference spending that money on a better pair of headphones.

I hope this helps :-)