I agree with many others here to start with the speakers and then match the integrated amp from there.
insofar as great Integrated Amps, I recommend giving the Krell K300i a listen. It is stunningly good and if you get it with the digital board, it will be a nice central piece to your rig. They can be found used at the top end of the price range you mentioned.
BYW, I own one and and loving it. 90watts into 8ohms Class A, then up to 150. In class A/B, doubles in 4ohms and doubles agin into 2ohms. It will drive anything and do it with authority, clarity, and great musicality.

