For fuel efficiency:
1. IN A JET, Achieve Best Rate-of-Climb Speed (varies with weight) ASAP so that you get to your OPTIMUM alt ASAP. Overall fuel burn will vary depending on if you are climbing into a headwind or a tailwind.
2. Above 10,000ft is NO guarantee that you are not going to have a birdstrike. This is a somewhat arbitrary figure based on stats. I personally have had a birdstrike at 21,000ft while climbing at 290 knots. Very fortunately, a glancing impact on the side of the fuselage.
So, you need to define your criteria.