Originally Posted by yoops /img/forum/go_quote.gif So out of
HD600, HD580, AKG K601, Stax, AKG K1000, AD700
which one doesn't require an amp or any extra hardware
Well, those are all over the board in terms of price range and requirements. Stax is a brand, not a 'phone, and all its headphones require amps...in fact, they're electrostatic, so they're usually sold with amps (and, if powered through an adapter, require speaker amps, not normal headphone amps). Those systems start at about $500 and run from there up into the stratosphere. The K1000 is going to run you $1000+ used (it's discontinued) and definitely requires an amp.
The Senn HD580 and HD600 are pretty much the same headphone, except the HD580 has plastic grills and is discontinued, while the 600 has metal ones (it does affect the sound quality) and can be gotten new. HD580s with HD600 grills and HD650 cables are a pretty common item on the FS forums...basically like getting a 600 on the cheap (around $150-$200). They also require an amp.
Your two remaining 'phones I don't know much about, except FWIR the discontinued AKG K501 is preferred for classical over the K601.
Honestly, rather than looking for your perfect headphone that doesn't need an amp (a very common newbie mistake), I'd figure out my budget for the system as a whole, and then budget that between amp, headphones, and possible a decent DAC. If you've got a situation that really doesn't allow an amp (really, really restricted portable setups or very, very low budget), it's understandable, but doing the ampless thing becomes impractical very quickly.
I have the ATH-AD700 and I bought them to listen to classical music. They sound good and I enjoy the music from them. Remember that they are open backed headphones (The A700s are closed headphones). I listen to flac files and I use a cmoy amp with them.