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Rather than spending money trying to get the most out of a mid-tier headphone(s), its more economical to go straight to the top, then slowly upgrade your other components up to par.
I agree with that, you're on Head-Fi, get a flagship headphone you know you will like. Be open to other headphones too, personally I'd take an Audeze or HiFiman over a Sennheiser anytime.
Headphone is still the part of the audio chain that makes the most dramatic increase/change in sound quality. It's also the thing I prefer to own and manipulate.
Once you'll like a Headphone, Kyle 491 said it, take your time working your way onto improving its sound (that's the lengthier quest). Plug it in everything you see with an audio jack and get a feel for which electrons would sound the best (what do you want, power, speed, extension, details, musicality, warmth, tubes?), that are good for your headphone (know your headphone). You will be able to read the review of an amplifier and make yourself an idea of the possible synergy your headphone could have with it.
Just make sure you buy the right headphone! Unless you are ready to feel regrets and sell it on the forums.
If you have money, go for it, even unamped... and don't wander around every other brands buying their mid to low models. If you're serious about it, and it will happen to most Head-Fi, you will want to upgrade, you will buy new headphones, and 2 years later you'll finally have a HD800 and feel like you've done a long way, (not) (you just lacked guts, and ended up paying more, desired many more things and tweaks, it took you time and plastic). That's what I did with Grado... should have bought that HP-2 already. End-game is end-game. Once you've found your love headphone I think the rest is fun (at least has been, and is for me).
Plugging it straight into you're iPod will not hurt the headphone. Listening to mp3s with a HD800 won't make you dislike your tunes, or make you want to start upgrading everything (file formats, computer, audio gear) compulsively, won't hurt your ears or your headphone either... I don't think you will get laughed at on Head-Fi either.
Now that this is said, you do, will want a amplifier (if you don't have a receiver or anything with juice) to get access to the higher and more exciting volume levels. Names of good entry amps has been given for the HD800, they will do their job and that's all you need to start with. But you can also buy the headphone before the amp, no problem to this.