Help me choose an integrated tube amp? OR separates

I'm going back to high efficiency speakers and a nice low powered tube amp. (Probably Tekton speakers)
I've come to realize that I like a little coloration and plenty of air.  So I'm assuming something SET or at least triode.
Must haves are:
remote
$4k or Less - less would be great :-) 
And I think I need HT pass through unless there is another/better option as I would like my front speakers to play double duty with my HT receiver and my 2 channel amp.
And I'll likely go used

I think that might be a lot to ask out of an integrated so I'm open to separates info as well. But the need for certain aspects of the amp and pre to match are confusing to me right now.
Maybe you can tell me what needs to match between the separates to have proper cohesion? 


I recently came across the Vac Avatar SE and seems like a pretty excellent option for me. But the HT RCA input gets called different things depending on where I read. It sounds less like a pass through and more like an option to use the tube amp as the front end of your HT/TV set up.
"In Home Theater mode, the preamp is disengaged, allowing control of the power amp by an external processor
 as the two-channel, liquid-cherry tube centerpiece of a 5.1-channel surround system."

Help!