Without scrutinising everything that has been said so far, I would like to simply put in my two pences worth.
The speed to use when calculating ROC is definitely GS. The Gadient is purely dependant on the rate at which horizontal displacement is made and the rate at which vertical displacement is made.
TAS is not a measure of the rate at which horizontal displacement is made, nor is IAS. Since wind velocity displaces TAS and pressure altitude and ISA temperature deviation displaces IAS, these cannot be used.
Text books which use TAS instead of GS will continue on to say if a wind is present the TAS has to be corrected for wind, which means you are using GS.
[Wing lift performance is based on IAS yes, (CAS more accurately) but this is still not a question of whether the wing can produce the lift or not, rather what GS and ROC translates to a particular climb Gradient. This is the job of the coming steps].
The pilot should work out the ROC required given the Gradient mendated on the departure and the expected Groundspeed on the climb out. Simply take the IAS you will fly as you climb, apply Pressure Altitude and Temperature correction (eg. using Flight comp) to arrive at your TAS, then use forecast wind to arrive at your GS. Then, Gradient * GS = ROC needed to meet this gradiant during departure. You simply fly the IAS on the ASI and ROC on the VSI (whatever power and pitch needed) and it will give you the Gradient you need!
However, you still dont know if your aircraft can provide this performance! At Max climb power, your climb performance will vary on the day based on weight, altitude, temperature (WAT), flap setting etc. Thus, you must then resort to climb performance charts to check if the ROC/Gradient required on departure is achievable on the day. If you have Climb Gradient performance chart, then you check if the Gradient is achievable, if you have a ROC chart, you check if ROC is achievable...
If ROC achievable is > ROC required, you are safe. Or if Gradient Achievable is > Gradient required you are safe.
You can then confirm using the following formulas:
If ROC graphs are available:
Distance (NM) = (Height Gain / ROC) * (Groundspeed / 60)
You can plug in Minimum Height to Gain over the obstace and see at what range you will be when you are at that height. If the obstacle peak is at 4NM and you need to be 2000' at 4NM, answer yielding 5NM is a problem because that means you will be below the required minimum height over the obstacle. Also:
Height Gain = (Distance * ROC * 60) / Groundspeed
Convenient because you can plug in 4NM and see if its 2000 feet and above or not.
If you have climb gradient performance graph then
Distance = ( Height Gain / Gradient) * ( 100 / 6080) * (GS / TAS)
and
Height Gain = (Distance * Groundspeed * 6080 * TAS) / (GS * 100)
Just as pointers, if minimum ROC/Climb Gradient cannot be achieved on the day, then you can adjust certain paremeters. Weather cannot be changed so Altitude and Temperature are fixed. Flap setting may be changed with due consideration to TORA, TODA & ASDA. Or you may wish to reduce the aircraft's weight either by reducing the Traffic Load, Or you may reduce the Fuel you are taking, bearing in mind not to go below minimum fuel required by JAR-OPS for the flight. Reduction in Weight increases climb gradient as Gradient = (Thrust - Drag) / Weight. Confirm by chart.
Take care.