I agree with all of this, but I'll build on it.
First is selection: He looks for players who are 1) team oriented; 2) will listen to him; 3) hard workers; 4) intelligent; 5) high character; good passers; 6) willing (and in many cases, eager) to play defense.
There are probably more. Talented, of course. He's not alone in looking for most of these characteristics, but I think he's a little more rigid about it.
He has a basic philosophy and model for how the game should be played, but he does tweak things every year to play to his players' strengths. His overarching game plan always relies on defense-to-offense and on passing. He loves bigs who pass (don't forget when Stef Dolson got the triple-double, she was so excited because it was points, rebounds, and ASSISTS). No WNBA coach doesn't want someone who defends and passes.
But I think the most important thing is the read-and-react that he teaches on both offense and defense. Many noobs in the W talk about how much there is to take in, new concepts to learn, but that's much less the case for UConn players. They're used to motion offense. They're always good at reading picks -- going above, below, or switching. They read passing and driving lanes well. They move their feet rather than their arms on defense. All sorts of stuff that comes from read-and-react.
And to build on what RSHERM just said above -- Geno, CD, and the whole coaching staff prepare the players for more than just what happens on the court. They're prepared for life, interviews, and other things that ease the transition to the W.