Desktop headphone setup advice

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I just purchased a pair of Beyerdynamic DT770 Pro 250ohm and I'm in need of some help with the rest of my audio setup.

Headphone Specs
Transducertype - Dynamic
Operating principle - Closed
Nominal frequency response - 5-35,000Hz
Nominal impedance - 250Ω
NominalSPL - 96dBSPL
Nominal T.H.D. - <0.2%
Power handling capacity - 100mW
Sound coupling to ear - Circumaural
Ambient noise isolation - approx. 18dB(A)
Nominal headband pressure approx. 3.5 N

Headphone Math

Power from SPL: Antilog((110-96)/10) = 25mW for DT770 to hit 110dBSPL peak
Voltage from SPL: Antilog((110-96)/20) = 5.0Vrms for DT770 to hit 110dBSPL peak
Using the Power from SPL to calculate the voltage required: V = (PR)^(1/2) = (0.025W x 250ohms)^(1/2) = 2.5V

FiiO E11
According to the FiiO website this amp puts out 300mW at 16ohms. Using these numbers I calculated the voltage to be at 2.2V. And by using this voltage and the headphone resistance I calculated the power with the DT770 to be 19mW.

According to the above numbers the DT770 250ohm needs 25mW and 2.5V in order to hit the chosen 110dBSPL peak. However, from what I've been reading people have been saying that the E11 drivers their DT770 600ohm just fine. Did I do something wrong with my math?

DAC
I will only be using the DT770's with my computer. How good is the DAC on the on board sound card compared to other sound cards?

Other Questions
If you have an external amp and an external amplifier then does the sound card even matter?
Is it a better idea to get an external DAC or a better sound card?

Shopping List (suggestions would be greatly appreciated)
Amp

FiiO E11 - Depending on what advice I get here I may not go with this amp. If it turns out that it can power the DT770's with no problem then it'll be hard to beat for the price. For $65 it comes with an extra battery and an external charger.

I'm not considering the FiiO E7 because there is just not enough power in it to drive my DT770's.

DAC
I'm not too sure what DAC to go with (if any).

Sound Card
I'm not too sure what sound card to go with (if any).

DIY
My soldering skills are pretty much nonexistent so I don't want to tackle any DIY project yet because it may take me awhile. After I practice soldering for the next month or so I plan on building the O2 amp.
 
Two issues:

Power from SPL: Antilog((110-96)/10) = 25mW for DT770 to hit 110dBSPL peak
Voltage from SPL: Antilog((110-96)/20) = 5.0Vrms for DT770 to hit 110dBSPL peak

Line 1 assumes "NominalSPL - 96dBSPL" is 96dB @ 1mW
Line 2 assumes 96dB @ 1V

The rated sensitivity has to be either 96dB @ 1V or 96dB @ 1mW, but not both at the same time. Throw 1V into 250Ω and it draws 4mW.

If not stated, I'd assume that sensitivity value is @ 1mW. So 25mW for 110dB.

According to the above numbers the DT770 250ohm needs 25mW and 2.5V in order to hit the chosen 110dBSPL peak. However, from what I've been reading people have been saying that the E11 drivers their DT770 600ohm just fine.

Case 1: Old music with uncompressed dynamic range
The music hits 110dB for just a short while the rest of the song is at a much lower level on average. The system may do fine for most of the time, and when it gets loud and distorts, the listener probably doesn't notice.

Case 2: Present-day music with highly-compressed dynamic range
The music has a peak of 110dB and an average of, say, -10dB relative to the peak. That is 100dB. Safety regulations require ear protection in places with constant noise levels over 80~85dB, this should illustrate how loud that is, if continuous. Few people I know listen that loud on average (after borrowing an SPL meter to probe around), and one shouldn't anyway.

Just measure yourself if you have a multimeter - adjust the volume to the maximum volume you can still enjoy the music at, then measure the output. If it is way below 2.2V, the E11 is driving the DT770 Pro just fine.
Edit: Set the volume while listening to your favorite piece, but measure when playing a 50Hz, amplitude = 1 (or 0dB) sine wave generated by Audacity or any audio editing software, and have your ears away from the headphones because it will get loud.
 
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