Best integrated tube amplifier, under $3,000.00. No phono needed. Could be used, too.d

Quicksilver. Hand made in USA and sounds excellent. 

Without question... the Line Magnetic integrated amps... will amaze you.  Just incredible resolution of detail, clarity, and 3d soundstage.  Those mentioned above are as good as it gets!

The Raven Audio Blackhawk has the best sound out of the box- truly high end rich yet transparent.
If you need more power the Rogue CM II/III can sound nearly as good with some tube rolling of the 5 small signal tubes.  
May have been supporting systems but I did not care for the sound of the Line Magnetic integrated amps.  
The Primaluna sound very good but tend to have a certain flavor to the sound and have too many tubes to deal with for me to bother.  

Here’s Huff’s review of the Line Magnetic amp, which sounds very much like their amps noted above. Though, I think I might even like the LM 518ia, or LM 805ia a bit better.

Huff kinda "goes nuts" over every new amp he reviews. But, you will have a difficult time finding a better sound than any of these Line Magnetic amps. Certainly for their modest price.  

Of course... provided... that you mate them with the right speakers (e.g.  Proac Response D2).

https://www.stevehuffphoto.com/line-magnetic-219ia-integrated-tube-amp-review-300b-and-845-tube-magic/

I can vouch for the Rogue Audio recommendations. I have a Cronus Magnum II and it's great!