A very intriguingly intelligent question. The average cruising altitude for long haul flights ranges from 30,000 to 40,000 feet depending on the capability of the aircraft.
Aircrafts are cleared to specified heights on each leg of their journey. The ATC will not clear a pilot to fly at 30,000 feet if Mt. Everest is in its route. They will either detour or climb higher.
Aircraft flying all over the world follow a 'quadrantal height separation' system under which each aircraft is allowed certain heights depending on their headings. Each heading has either 'odd' or 'even' thousand feet, or 'odd +500' or 'even+500' thousand feet height allocations. (Degrees - 000-089 even, 090-179 even+500, 180-269 odds, 270-259 odd+500)
Average time to reach a cruising altitude would average between 15-20 minutes depending on very many factors. The clouds you refer to are "Cirrus" which are found in the higher altitudes, even above 30,000 feet (the cirro-stratus).