The amps that are recommended are all good but not what I would focus on. A friend of mine is friends with the Woo designer and told me recently that Woo has a new amp that is killer. However, I say forgot all of those because a phone is more important and should constitute about 90%+ of your budget.
The Schiit AsgardX (mentioned before) or the Schiit Mjolnir v3 amp are under $1000 and get you to a very high level of performance. Use most of your funds on a phone.
The place to learn about these things is at the head-fi web site. You can also get any phone you want a decent used price.
Recently, I had one of the very best headphone amps in my home for a few weeks. The Allnic HPA 15000 OTL/OCL. This thing is incredible and very expensive ($15k). Even though it was better than the 2 Schiit amps I mentioned (AsgardX and Mjolnir v3), the phone was still the most important thing. I say this because I also had a demo RAAL 1995 Magna phone ($7.5k) in the house and I tested it with the Allnic and also my Schiit Aegir v1 amp ($400 used). With the Magna the Allnic was better but the Schiit was not embarrassed. If I had not heard the Allnic I would have thought the Magna and the Aegir v1 combo were end game.
