Hi Crosscheck,
I'm sure someone who uses the default 777 will come on and advise you the exact rate of climb you're asking but I'd say in general that part of the learning is realising the limitations of each plane that you fly.
I'm sure you'll be aware that all planes have stall speeds, that is, the speed where the aircraft is no longer going fast enough for the wings to generate lift to make flight possible.
The rate of climb must as you say be controlled in order to climb safely to your target altitude. The nature of aircraft is that the higher the altitude, the gentler the rate of climb required, in order to avoid losing airspeed and possibly stalling.
A great way to test this is to load up a plane, find out it's clean stall speed (The speed it will stall with NO flaps), take-off and start climbing....
Now aim to keep the speed at this stall speed + 30knts....
You'll find that the higher you are, the more you'll have to reduce your rate of climb (Vertical Speed) in order to maintain that target Airspeed.
This is the best way to "Stay on top of your" rate of climb.... monitor the plane's Airspeed and use that as your guide for your rate of climb (aka. Vertical Speed).
If the Aircraft's Airspeed starts accelerating to high speeds, increase the Vertical Speed rate, if it starts decelerating towards too low a speed, reduce the rate.