who makes a good set of headphones

Suggest you also visit headwize.com. Use the search engines at these sites to limit the amount of time you spend. You can spend days researching this and will not find any clear consensus except that Grado's and Sennheiser's are good headphones. Headphones are a very personal choice because not only sound quality, but comfort matters and everybody's heads and ears are different. Sennheiser's are more difficult to drive and usually need a headphone amp, probably with tubes or from Headroom to sound their best. While most headphone amps sound better than the jacks on most tape decks and cd players, I have gotten very good results using the headphone jack from an NAD receiver.
I use Grado RS-2 and Ultrasone HFI-600 headphones.
Their are a lot of reviews and comments on available on the Grado's. Their lower priced 'phones are great values and the higher priced ones are a little more detailed and richer sounding. Many people don't like the way Grados feel on their ears, but you may want to try the "comfy" ear pads before giving up on them.
The Ultrasone's are a German headphone aimed primarily at the pro audio market and are not well known. They are smoother, more spacious and more refined than Grado's or Sennheiser's but are not quite as detailed and sound laid back in comparison.

I personally have liked Grado headphones. I have owned the RS-1's and RA-1, SR-325's and SR-80's for portable use. I have also owned Sennheiser HD-600. All excellent headphones. In my experience you can get away without an amp with Grados as they are quite easy to drive but not so with the Sennheisers. I'd recommend the amp though if you really want to hear any headphones at their best. Among the choices you mentioned I think your choice will depend also on the type of music you listen to. The aluminum sound chamber on the 325's does sound quite different than the plastic of the less expensive models. If you listen to classical I'd suggest you go to the RS-2 (I think you can get them used in this price range) as the mohogany sounds better, at least to me, with "acoustic" music. If your budget includes the amp then go cheaper, get and amp then change the 'phones later.

Grados are excellent headphones but wearing them and keeping them on the head for a long time is a hell of a pain.
Senheiser HD-600 are not close to the quality of sound to the RS1 but great to wear and great value.

Stax is the world ear standard that designes great headphone with their own drivers and to me I believe that Stax combines the comfort of Senns and quality of Grados.

I have a combo Stax Lambda with Stax SRM1 headphone driver that plugs in to either tape output of the preamp or any line output of the source.

Through the headphones you can even more hear the small-tiny differences and noises. When I listen to the records through the headphones I specifically and thoroughly clean them with VPI before spinning. Anything imperfect can be opened through the headphones and that's why a dedicated headphone amp is important or a dedicated high quality built-in unit can also be helpful.

Very often for the headphone output manufacturers just place the matching transformer from the basic preamp circuit to go cheap and this solution drives listeners off getting onto headphone systems due to the high level of noise and distortions of transfered signal. Many preamps or sources with built-in headphone output can't handle high impedance headphones such as Sennheiser HD600. Grados are low-impedance headphones that can probably perform OK with built-in outs but having their dedicated headphone amp you can gradually hear a bunch of differences. Grado headphone amp at the same time absolutely helpless to drive Senns. That is sought in volume control when you realy don't understand which volume position where you can have a full range without even speaking of music huh...

So headphones with the matched headphone amp can give you and will certainly give you more defined and holographic music than any any speakers.

I have a Musical Fidelity tube headphone amp with Grade sr 125 headphones. sounds very, very good; so good I wonder why I have these big speakers and amps sitting here since I am the only one that usually listens to the stuff.

MF Can ver2 amp and Sendheiser 600 headphones sound very very sweet. I changed the tubes to Amperex and it sounds even better.