If you do not want the most comfort possible, disregard my suggestions. I have been data logging homes for the last 20 years and I can assure that when the outdoor dew points are high without high cooling loads, your home will become damp inside unless you have some supplemental dehumidification. During low dew point weather, it is not a problem.
A single speed a/c setup properly will maintain <50%RH any time it can operate for 3-4 hours. As the hours pass after operation, the indoor moisture will rise to above outside levels depending on the number of occupants and the amount of ventilation/infiltration amounts.
Multi-speed and even the VS a/cs are unable to remove moisture with a significant cooling load. The a/cs remove 1-2 lbs. of per KW, while high efficiency dehus remove 4-7 pints of moisture per KW. For the price of the multi-speed a/c, you can have regular a/c and a small whole house dehumidifier. Check out the Ultra-Aire/Santa Fe/Honeywell etc.