I may be wrong but I learned that in regular airliners, pilots always takeoff manually.
After taking-off and going to a positive rate of climb:
- When do pilots engage the autopilot?
- Is there a minimum altitude to engage it?
The minimum altitude for autopilot engagement is generally the acceleration height or around 400' AGL though this can vary between operators.
The question of when the autopilot is actually engaged is a more complicated question and is subject to pilot preference. Personally, I generally hand flew until the first level off or until climbing and accelerating through 10,000 MSL. Others may turn it on as soon as allowed and most fall somewhere in the spectrum between the two.
For me, it was a question of how close you were to your 6 monthly Sim check. The closer you were the more handling practice you gave yourself.
In general, on a normal line flight, I agree, around 400 feet on acceleration and as the BAe 146 had no Autothrust I generally hand flew most of the approach from decelerating, taking flap 18 and putting the gear down. It was my feeling that a human pilot coped better with configuration changes than the autopilot and with no autothrust I wanted to be completely in the loop and therefore, completely flying the aircraft rather than having the autopilot take care of 3 axes and juggling the thrust manually.