Is it better to run the fan constantly, and if so should it be a multi-speed type that is most efficient for the central air conditioner?

For A/C it is not better to run the fan all the time unless you have a controler to modulate the motor speed. If the A/C is left on high speed all the time it will just some what rehumidify the air in the area being conditioned.

If you have a controler that will take the blower down to its slow speed it can be beneficial.

Go here for more information and the proper way to control that motor.

IAQ Direct - FanHandler Introduction

If you are referring to the fan in the a/c there are reasons to operate the fan, obviously it costs more to let it run constantly but you get a more even temperature in the areas served and you are constantly filtering the air especially if you have a high efficiency filter.

All running constantly does is circulates the air. For this I would not mess with the fan speeds.Many folks preferr to let fan run. I have run mine both ways, constant and auto and noticed no difference in elec. Bill. Another thought is to run on auto and add ceiling fans.