I really wouldn't care which side of the ball he came from or whether he was a coordinator or not.
I want a HC who has some real emotion for the game, a great motivator who inspires people to play beyond their abilities. A man who understands how hard you have to work to be successful in this profession. A man who can delegate authority but still has the ability to make input on both sides of the ball. A HC who likes to teach and isn't too aloof to get dirty with his players if it is necessary.
I would never give my HC control over the draft, my GM would handle that aspect of the job with some input from the HC but the GM retains the last decision on any player drafted.
I would give my HC Carte Blanche in his first year and I would live with whatever record he produced as I would expect him to clean house and get rid of the deadwood. I would expect marked improvement in year 2, somewhere close to a .500 record and in year 3 I would expect a serious playoff run. Most of the great HC's have followed this pattern and I'd be watching to see if my new hire did so as well.
During the interview process, I'd be looking for an intelligent HC who realized how to build a winner and I'd ask him what his plans for the team were for the next 3 years. If his plan didn't correspond to mine in any way, it is doubtful I would hire him. I want a realist as my HC not some pie in the sky type.
And proud of it!!!