The plumb bob is the most commonly used tool for monitoring the verticality of a building under construction. Two plumb bobs at at the end of each face of a building, Extending up to a fixed height from the base of the tower, so that same reference points are used at all time, can give the best result. Using the plumb bob i could complete the construction of a 80m tall rectangular structure at a cement plant, within the specified tolerance of H/1000 with ease.
Alternatively total station also can be used for monitoring the Northing & Easting of the four corner of the building at each level.To achieve this four reference pillars / fixed station are to be established on the ground away from the tower, from where the corners of the building can be viewed thro the telescope of total station till the building reaches its total height.
If it is possible to instal permanently, the laser plumb can be used for measuring the deviation. The tranmiter is to be fixed at the base and the target glass plate is to be attached to the moving form work permanently. This method is used in the construction of circular silos / Chimneys wherein the slip form method is used for raising the RCC tower.
For the affordable GPS may handy with proper integration. I am yet to try this, no idea about limitation & cost.
I hope the above is of some use.