If you are thinking of changing your speakers, I would make that decision first. Only then would I start looking for an integrated that pairs well with the speakers.
There are a lot of very good integrated amps in the $1500-2000 range (new - I won't speculate on used prices). Just off the top of my head I can think of the following that I have heard or owned: Exposure 2010S2D, Naim XS2, Musical Fidelity M3si, Yamaha AS2000, Rogue Sphinx, Croft Phono Integrated, NAD 377BEE. They all have strong points to recommend them - it's really a matter of matching them with the speakers you have and finding a sound that you like.
I'd read up on the various reviews for an amp in the power range you are looking for to narrow down the choices. Then demo if you can. If you can't demo, look for a good price on a used unit here on Audiogon and give it a go.
Have fun! Scott