DT 880 Amp w/ DAC Help

So Im super super new to this whole audio thing. I did research all day and im stumped at this particular thing. I plan on getting the DT 880 Pro headphones 250 ohm version. I plan on using the headphones for 75% gaming. And it was recommended to me that I dont get a gaming headset as the quality was bad. I also plan on using studio speakers. I dont know which to choose, I have Audioengine A5+ and M-Audio BX5 D2 in mind. My problem is that it was told to me that I need an amp to use to the 880s and then I was told that I would be able to use an amp+dac box with the Audioengine A5+ because it already had an amp built in and it would conflict and stuff. I dont know if its true. But I am looking at three products for amps and dac. The main one I am looking at is JDS Labds o2+adac for $280, and the other two are the Focusrite Scarlett  2i2's(I dont know if its an amp as well) and the audioe engine d1(dac only I head?). What I want to know is which is needed for the best quality out of DT 880 Pro? Does the 880 Pro even need an amp? is the 2i2 an amp and dac? Just amp? Or Just DAC? Is the d1 enough for the 880 pro as just a dac? Also have speaker questions. I understand that the speakers will always be default, but if I connect the headphones do they automatically mute the speakers? Is there a way to have both headphones and speakers connected and just disabling one using software? Thats it for now. Any help is appreciated. Any other product idea would be idle to, Im not set on just these, just what I could find. Thanks. 

Anything >

Does the 880 Pro even need an amp?

Yes. While the DT 880 may be useable with some onboard audio, you need an amp to get the most out of the 250ohm varient, unless you happen to have a motherboard with high end integrated audio. (these are few and far between)

is the 2i2 an amp and dac?

No. It's a mic preamp for recording.

Just amp? Or Just DAC?

You can use some amps with your PC's standard 3.5mm output jack, this may not be a bad option if your motherboard has a decent audio codec like the Realtek ALC89. You cannot use a discrete DAC without an amp, as the extremely high output impedance on most standalone dacs will cause distortion.

  Is the d1 enough for the 880 pro as just a dac?

The D1 is an amp/dac all-in-one, I don't have any idea why they don't advertize it as such.

but if I connect the headphones do they automatically mute the speakers?

To use your speakers, you will need to use either a male to male 3.5mm audio cable which can be connected to the headphone jack on your PC or an amp, or RCA cables, which you will need an external device for. If you have multiple devices receiving output from your PC, you will be able to select which device you wish to use. For your situation, I would recommend that you consider the audioengine D1, which has a 3.5mm jack for your headphones, as well as RCA output for your speakers.

 

The D1 won't have enough power to drive those headphones. They barley get my AKG K612's loud enough.