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In general, amplifiers help. They can increase soundstage, tighten up response and generally provide better clarity. This, however, does depend on your headphones. Some headphones, like Grados, are low impedance and high sensitivity, so they can be driven easily and do not need amplification (though Grado owners do report some small benefits to be gained from amplification).
In your case, Sennheiser HD 558 have a 50 ohm impedance, meaning they're harder to drive than Grados. To be honest, I haven't listened to a pair of 558s, so I don't know to what degree they'll benefit from amplification, though I'm sure they will at least a bit. I own the HD 650, which definitely needs amplification to sound its best, but that's a different animal altogether. Hopefully somebody with 558s can comment.
Here's the part where I talk about stuff that doesn't pertain to your question.
A few other things to keep in mind:
-Garbage in, garbage out. Hence, you'll gain the most benefits in sound quality from upgrading your source. That is to say, if the files on your iPod and laptop are in low-bitrate mp3 format, it's not a bad idea to rip from CDs and get your collection in 320kbps mp3 or FLAC (or, in your case, ALAC, which is compatible with your iPod:
http://en.wikipedia.org/wiki/Apple_Lossless). CDs are awesome and have excellent sound quality, so no worry with those (but for the sake of convenience, it might not be a bad idea to rip them to a lossless format, FLAC/ALAC).
-The next most benefit you'll gain is from your headphones. Upgrade your headphones first before you upgrade the other parts in your chain. The only thing you'll have to be cognizant of when doing this is to make sure that you don't get headphones that require amplification to sound good, unless you're planning to also invest in an amplifier at the same time.
-After the source and the headphones, the next things that are important to upgrade are your amplifier, and then your DAC. So, in order from most important to least important: source, headphones, amp, DAC.
-Despite this, however, it's important to note that your audio is the sum of all elements in your chain. There is always the possibility that one of the elements can hold back the entire system - that is to say, the proverbial "weak link". When you make your upgrades, always aim to eliminate the weak link in the chain.
-Tweaks like vacuum tubes (for tube-based amplifiers/DACs), cables, power components come at the very end. Tube-rolling definitely has an effect on the sound, but it's a trial-and-error process to figure out which tubes suit your ears the best. Cables and power components (line conditioners, etc.) have a questionable effect on sound. To elaborate, some say they change the sound and others say they don't, and there are large contingents of individuals on both sides of the battle line. In order to avoid inflaming people and starting yet another skirmish on this topic (and believe me, there have been many), let's just say the topic is controversial and hotly-debated. At any rate, don't spend money on this stuff until much later.
-Trust your ears. A lot of people will tell you a lot of things, but you're the final arbiter of auditory truth and justice. Pick what you like and what works for you, because nobody can tell you that.
For your iPod, I'd look into these:
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http://en.wikipedia.org/wiki/Apple_Lossless
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http://redwineaudio.com/products/imod or
http://www.whiplashaudio.com/personal-players/whiplash-audio-whipmod-upgrade-service.html (or there's a DIY mod that's similar, if you have the capacity to DIY)
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http://aloaudio.com/alo-audio-imod-cable-v2-lux-fep-18awg-occ.html (Note: This thing is mega expensive, and there are much cheaper versions of these floating around. Keep an eye out for LODs.)
Whatever you end up planning on doing, figure out what you aim to get out of this experience. You don't necessarily need to spend a lot of money to significantly improve your sound quality, but if you get sucked in there's a good chance you will end up spending a lot more than you initially wanted to. Set budgets, don't spend outside your means, and don't be reckless. If you have questions, always feel free to ask, and don't feel your questions are stupid or not worth the time. This community is a vast resource, so use its existence to your advantage. And if you can DIY, that's where you'll get the most bang for your buck, hands down.
I'm aware I've given you a lot of information above and beyond what you asked for, so feel free to ignore the stuff you feel is not relevant to you. Whatever IS relevant, I hope it helps.
Welcome to Head-Fi, and sorry about your wallet!
Edit: Just reread a little bit and noticed you cancelled your Sennheiser HD 558 in favor of Audio-Technica ATH-M50. They're easy to drive and don't need amplification, but will probably benefit marginally.