The available motor power is possibly the first limit on the speed that an axis can reach. Yes the screw will tend to whip and this is undesirable. The size of your machine indicates that lead screws will need support at both ends. If you are going to use stepper motors there is a rapid loss of torque as the motor speed increases. Yes the very coarse pitch multi start screws require a slower motor speed to achieve the same rate of feed as a finner pitch screw, Thus there is a balancing act between the stepper motor torque fall off as the speed increases and the pitch of the lead screw. Obviously some form of gearing between the motor and the screw can help provided the motor has enough torque.
A good place to start is the paper by Irving2008
Irving has also produced a spread sheet which takes the tedium out of the necessary calculations and this can be found in the above tutorial.
Hope this helps get you started in the right direction - Regards Pat