I was surprised when I noticed that the specs sheet states it doesn't need an amp. I took it for granted that it would need an amp anyway. Sorry.
Although I dislike cnet reviews for audio because they're very commercial (it's somewhat better for speakers), this report is adequate: "The HE-400 headphones are designed for use at home with a receiver or headphone amplifier due to the drivers' increased weight, but they can work with portable devices; the only drawback is that you'll experience limited volume capability with a weak-powered mobile device." Link: http://reviews.cnet.com/headphones/hifiman-he-400/4505-7877_7-35182256.html. Whilst I doubt it would sound so good off a phone, it would probably sound fine off a laptop. Try it without an amp, and add one later if you think it's needed.
As to DACs, I'm not "converted" yet. Many DAPs have acceptable DACs, and many computers have at least tolerable soundcards. A good soundcard is generally a better investment than a stand alone DAC. Moreover, a DAC / soundcard is obviously secondary to any amping you might want.
But I do believe in burn in, especially with pink noise. We just had a friendly argument about it (http://www.head-fi.org/t/696168/do-i-really-need-to-burn-in-my-headphones) that shouldn't be rehashed here. So read that thread, and decide for yourself which arguments you find persuasive.
I think that is what I'll do. Buy without amp first, and see how it is, and then later on buy one. As for a sound card I don't really have a dedicated one, I currently just use whatever is stock with my motherboard. Also, what is a DAC, and what is the difference between that and an amp?