Let's say for a headphone that costs about $100, I'm guessing your budget for a USB DAC / headphone amp is maybe $100 or less.
Also you gotta know that these USB DAC Amps sell in a price range of literally $6.49 USD for the Sabrent AU-MMSA to well over $6,000 USD. So requesting "the very best usb soundcard" will no doubt cause a flaming war in some circles. I don't recommend the Sabrent, btw, and that's just me.
So I'm figuring you want a real, no-nonsense answer, and that this is not troll bait. If that's correct, then in my humble opinion I suggest:
Many people are very pleased with the Audioquest Dragonfly Black, which can be bought for about $100 USD. And, you'd find some folks that would say it might be the very best soundcard for your headphones. Many of the FiiO products also have a large number of fans, I'm thinking the FiiO E10K, about $75 USD, for example. Even has a switch for added bass. I don't personally own either, but they are highly regarded.
That's two suggestions out of hundreds of possibilities. Everyone will have their favorite. Depending on how far you want to go down the audiophile rabbit hole, there's more research you could do here to know for sure. If you're interested in finding out more, there are several forums including this board, HeadFi, and others with literally weeks of reading available to you on the subject.
For example: For my own use, I answered your very same question by getting a Chord Mojo. I love my Chord Mojo, and wouldn't trade it for a basket full of others, but your mileage may vary. (I've been playing Prey with it, and makes the hair stand up on your neck.)
You'll find others who own more expensive DAC Amps and their answer to your question would be different than mine (see previous posts). Then there's Benchmark, Bryston, PS Audio, etc. etc. and on up the price tag ladder.
What's best for me, might not be what's best for you. Or anybody else. Ultimately, you get to choose. Yay! Enjoy!
Going insane (mite like better headphones) Antelpoe /prism $5000+
There loads of other's But take loook at the muse stuff on ebay its good vaule and sounds really good!!! (and prob in your buget buy your other gear)
I use Soniflex dac1 4 resons this suits me but if you headphone and laptop its not lot of use
2)has blance pro line out
3) high power headphone output
4)cheep on ebay less than $100
You need to work out few things
2) Input (usb prob) could be tosh/ Sdiff/fireweire/Aes 3 / ethernet (network)
3) Output some headphone reqiue high output / line non / blanced / pro line level
4) form (I want rack) if laptop you may want smal box with no power
5) Not all usb is equall some stuff need to much power for laptops will you need power brick or lead
6) And dont forget Drivers USB should just work but if flaky it as good usless Win 8 and vista had mega problems (early on before updates)