Ok, take a PA-28 and stand it on its tail pointing straight up. Put an engine and prop combination up front that can generate enough thrust (or force) to overcome the aircraft weight (plus any drag generated when it starts to move). Voila! Best angle of climb = 90 degrees and only requires that thrust exceeds weight and drag. The Americans experimented with this in the 50's with vertical take off prop aircraft (google Convair XFY).
The higher you climb, the more work is done because: work = force times distance. However, the rate of climb in terms of height gained in a certain amount of time could be pitifully slow.
To get a half decent rate of climb you will need an excess of power because power = force times distance (work done) divided by time. Or more specifically, an excess of power available compared to power required.
Does that help?
BJ