You're going to love the Uni-Fis and congrats on the new system. I believe your proposed setup will work just fine.
I have the Uni-Fi bookshelves with a NAD C 326BEE and they sound great.
You might be told the Uni-Fis need lots of power but that depends in part on room size, how loud you listen, the type of music you listen to, and how far away you sit. My man cave is 14 X 14 (yeah, I know square is not ideal but its what I have) and my main listening positioning is 8 feet from the speakers. I listen to mainly classical rock and some classical and I have never driven the Uni-Fis to the point where they have strained.
For the room you describe, your amp should be more than adequate.
FWIW, I have also had the Uni-Fis hooked up to a NAD C 275BEE amp (150 watts X 2) and I couldn't hear any difference from them being driven by the C 326BEE. Not a scientific test by any means and I'm not a "golden ear" by any stretch but those were my observations.