USED -- Aerial 10T < $2,000
NEW -- Event Opal $1500 each, but no need for amp as they're active
USED -- Accuphase E303 can be purchased < $2000 in perfect condition restored or serviced
NEW -- Bel Canto S300i
Excellent monitors that can be had for 2k new are Fritzspeakers and Selah.
Used speakers an integrated at that pricepoint very numerous.
Since your postings make it appear as though you are starting from the ground up, I'd find some speakers first, and I might tilt the allocation towards the speakers.
Don't have any favorites in all cases.
It all depends.
Integrated amps are as much about features as sound quality. The best one will depend on needs.
If building around speakers, OHM offers unique products with unique attrbutes I find to ultimately be the most listenable. There are many other more conventional lines I might vote for depending if the OHM omni sound were not one's cup of tea.
For a SS integrated with phono I would vote for Rogue Sphinx.
For an integrated with built in DAC I would lean towards Bel Canto or Wyred.
For a traditional integrated with no phono or DAC, I'd likely stick with good old NAD.
For a low power tube integrated for use with high efficiency speakers that I have heard and liked, , I'd lean towards Glow or Jolida FX10. Decware would be another consideration but have not heard those. Audio Note Kit pre-built another but would likely run a bit more.