Hello everyone. So I recently jumped on a chance to get the Beyerdynamic DT 990 Premium 32 ohm for fairly cheap. Only problem is, I currently have no amp outside of a mixer amp I have for PS4. I will primarily be using these headphones for gaming on my PS4, watching tv/movies on that and an iPad, and listening to music through an iPod. So I have a few questions.

I hear the trebles can be quite harsh, what would be a good amp to get that's not too expensive that'll tame those trebles, bring these headphones to life and not cost too much? I've never bought an amp before so I don't know where to begin. I'm thinking I'll have a budget around $100. Do I need a DAC as well?

This is the mix amp I have for PS4: http://www.plantronics.com/us/media/media-resources/literature/computer_audio/rig-surround_ps_en-us.pdf . Will the headphones work at all with it? If not, can I connect an amp to the PS4 (as I said, I'm new to the world of amps)?

Lastly, am I good with the 32 ohm version? I've heard some say the 250 and 600 versions are better while others claim there's not much difference. Or should I maybe consider trading for 880s? As I said, I want to use these mostly for gaming and movies/tv, but I also am huge on music and love everything from rock to jazz, r&b and hip hop, classical and world. I hear the 990s are very fun, so that makes me excited for gaming and movies, but because I listen to some classical and jazz, I almost want to consider the 880s. What do you think?

Thank you all for the help. My apologies for having so many questions.

So after doing a bit more research, I'm sold on buying both a DAC and amp for my 990s. My only question is what DAC/amp combo pairs best with the 990s? The Schiit stack looked appealing, but I've heard some say tube amps might be better to warm the trebles since the Schiit stack is pretty bright.

If you want headphone surround sound, with headphones connected to the PS4.
Get an Astro Mix-amp and FiiO A3 headphone amplifier.
The Mix-amp on it's own might be able to drive the 32-Ohm DT990.
But you would have the option of daisy chaining the FiiO A3 off the Astro Mix-amp.
The FiiO A3 could also be used with the iPad and iPod.
 
If you do not care about headphone surround sound, so you ok with stereo audio, then you can get a Schiit Modi, with an optical connection (instead of getting the Astro mix-amp).
And connect a headphone amplifier to the Modi, FiiO A3 or other.