I would expect a new FO to enjoy the flight as much as I do. Not to hesitate to fly the aircraft manually when convenient to build his confidence on the machine, to share his experience and to ask questions; I would be more than happy to answer and if I don't know we would check in the books together or ask on PPRuNe xD. I expect him to be relax but to be assertive and call my attention in case I'm doing something unsafe or stupid. I believe we can always learn from our colleagues regardless of their experience. But I also expect him to comply with the SOP and not to break my nuts when I'm flying unless it's unprofessional or safety related obviously. I always let the FOs fly the way they want, so I expect the same treat.
I expect him to be respectful and a good professional also. What grinds my gears for example is when I'm PF and I go to the toilet, as soon as I close the door, I can hear the engines spooling up... Cause he wants to go home early so he accelerates without telling me to gain 3 min of flight time and burn 100 kg extra fuel when we are 25 min ahead of schedule... Well done.