if you're going with noise cancelling, you won't ever have to worry about the other stuff, like an amp, DAC, etc.
Noise canceling, to put it bluntly Fs up the sound. Its subtle, and in certain situations, the benefit from noise canceling outweighs this coloration.
Here is my advice:
1) buy an entry level type high quality headphone. I own these two currently, and would highly recommend them.
a) Grado SR60 or Grado SR80 - This headphone will make it sound like you are on the front row and it just makes good music, particularly rock, come alive. However, they don't block out much, if any outside noise. However, I think most people tend to overestimate their need for blocking out outside noise. I know I did when I first started looking at headphones. However, for my money, this is simply the best sound you are going to get for under $100, without an amp.
b) Denon AHD1001 - Great bass. A little less forward the the Grados, they maybe sound like you're on the 10th row (not technical at all, just trying to convey the feeling). THey aren't as "sharp" sounding as the Grados either. However, they do sound fantastic and are easily driven by an iPod without an amp. And its virtually impossible to beat their comfort in the price range.
2) Figure out what you want to do from there. Really, after buying a good set of headphones, it becomes as much of a hobby as it is about improving the sound quality of the music. The difference between a low level pair of Grados, Denons, Audio Technicas, etc is just gigantic compared to what you are probably used to.
3) either buy a cheap, portable amp, something like a FiiO E5 or try out an amp, if that's an option. Also a possibility here is listening out of a receiver, as this will give you a rough approximation as to what your headphones will sound like with an amp. If you think it sounds like night and day, then:
4) Buy a decent DAC and amp, or possibly even a combo.
But my main point is buy a nice pair of entry 'phones first. Savor them, then see where you want to go.