For PPL I teach the following rule of thumb. After lift off accelerate to Vy and hold untill 1000 AGl and then transition to a cruise climb which is that speed which will maintain a rate of climb of 500 feet per min for the existing conditions. This speed must be at least 10 kts above Vy for engine cooling and forward visibility. If a speed lower than Vy + 10 is required to maintain the 500 FPM than reduce then reduce the rate of climb to preserve the Vy +10. When the aircraft ROC has reduced to 100 feet min at Vy + 10 (corrected for altitude !) you have reached the practical operational service ceiling for that flight.
For descent I tell my students to leave the throttle at the cruise RPM value and set and trim a descent attitude which will give a 500 FPM rate of descent, monitor the ASI so as not to exceed VNO or Manoevering speed (if applicable). Enrichen the mixture slightly and reduce the throttle as necessary as the aircraft descends in order to maintain the same cruise RPM setting. As the destination is approached reduce the airspeed to an appropriate value to enter the control zone/circuit.