As always, "it depends"...
In general, however, the maximum rate of climb airspeed (Vy) will yield the best fuel economy. The reason is that the engine burns substantially less fuel at higher altitude, so the quicker you get to optimum altitude, the lower the burn rate will be.
Climb winds may have an effect on overall burn, but it is still advantageous to get to the optimum altitude -- considering winds -- as soon as possible. Any lower altitude will, by definition, be less than optimum.