Need Audiophile Headphone Rig to Replace Sen HD590

My Sennheiser HD590s are in for repair, but frankly, even if they cannot be repaired, I may replace them just because I have had them for many years and I would like to explore what else is out there.

Let me give you my background. I am a serious audiophile and I listen to two different systems. The first is my master system which features a dCS Delius DAC and Purcell Upsampler, a gigantic monstrosity of a Mark Levinson amp, B&W Nautilus 802 speakers and very good cabling throughout the system. Needless to say this is a first rate system.

My second system features a Threshold T2 preamplifier, a Bryston 3B ST amplifier and B&W Nautilus 804 speakers.

My musical taste centers around jazz, folk and classic rock.

I have never used headphones with either of these systems. However, because I am temporarily living with people who are students, need quiet ect, I am now interested in occasionally using a pair of headphones with these systems. Note that neither system has any sort of headphone jack or headphone amp.

Generally my headphones stay in my computer room, connected directly to a Soundblaster X-FI sound card. I got awesome reproduction of game sound effects and ambience with the 590s, and I’d like to take things to the next level. I am considering the HD600s.

Suppose I wanted to take my headphone performance up a notch or two, but not spend a fortune. What cans would you recommend and if an amp is required to drive those cans, what amp? I would like to keep this project as affordable as possible--$600 or less including the amp if necessary. But I wouldn't mind spending less if possible.

I do want a significant improvement over the 590s.

Any thoughts? I think the cans will be HD600s but I don't know of any good, affordable headphone amps.