What is the average time and distance needed to reach cruising height?
I answer directly to the title of the question:


  What is the average time and distance needed to reach cruising height?


The Takeoff takes very little time, but the climb phase depends on the cruise flight level clearance. Assuming you climb with a vario of 2000ft/min with an average IAS of 200kts. The time to reach the cruise level is equal to:

(Cruise level in ft - takeoff terrain elevation if ft)/2000, the result is in minutes.

So if the departure is at sea level and the cruise altitude is at 30000ft, the climb phase will take : 30000/2000=15min

The descent till arrival could be more complicated because in addition to the pure descent you have to level before intercepting the approach phase which occurs relatively at lower speed. If you are lucky, not having to hold above the airport, the total descent might take 20 to 30 minutes

Routes are not necessarily straight lines, nevertheless you may assume an average cruise True speed of 500 knots.