I've attached a rough & ready method which seems to give useable results. I don't claim any credit for the 'calculation' - it was taken from a book much, much older than I am. I've typed it up for you because I don't have a scanner at home. The example is for a two-stage starter, but it looks simple enough to extend it to include a third stage. The supply was 120V - you will need to substitute your own voltage, current, and resistance.
At rest you have all starting resistors in series and the back EMF is zero, so you can apply Ohms Law to determine your overall starting resistance if you know the maximum acceptable current and the supply voltage.
For a two stage starter the author suggests the starting resistance is split into two stages of 75% and 25%, shorting out the 75% stage first. For a three stage starter he suggests 65%, 25% and 10%, shorting out the 65% stage first. The crude assumption made is that during each acceleration period the armature back EMF rises to a value equal to the voltage applied to the armature terminals at the start of the stage, which is not true. Purists will rightly say that this method has some glaring errors in terms of motor theory, but the approximations don't seem to result in a wildly wrong solution in practice - I found it was slightly conservative on a DC pump starter which I had to rebuild.
You could almost certainly model this in Mathcad and get a far better result: if anyone has time to try I would be interested to know how accurate (or not) the method in this old book turns out to be.