I'm not an HVAC expert, but I'd opt for the 2 stage unit. The problem with running a dehumidifier in the house is it puts out warm air. Generally not a problem in a cool basement, but not helpful in your living space when you're trying to air condition it as well. I think you'd be better off not letting the house get as warm and humid during the day then trying to cool and dry it out every day. Running a dehumidifier in living spaces is kind of like running a window air conditioner inside the house. You don't have the benefit of the cool air because the coil is inside the single unit, unlike an whole house AC unit that has a coil in the air handler to cool and dry the air and the compressor outdoors to expel the heat. With a dehumidifier it is all in one coil, cold up front to capture the humidity and hot in the back (exhaust) to start the cycle all over again.
On a somewhat related note, have you checked the house for insulation levels and air infiltration around windows, doors, attic scuttle hatches, plumbing and electrical holes from the crawlspace and attic? As part of your AC upgrade you might want to have a blower door test done to see what the air exchange rate is on your house and find the leaks.