There are pros and cons no matter what choice you make. The electronic air filter will use electric energy to function, as would a HEPA also drive up system static which means increased fan energy - both options that way use more energy. In this area (as others) if it were me I would follow the KISS method and and simply go with a good quality traditional filter. This keeps front end costs down, keeps ongoing energy costs down, avoids bothersome ongoing electronic filter cleaning, avoids costly HEPA replacement. IF there are family health issues such as allergy or other respiratory illness or immune sensitivity then everything I said is out the window and the priorities shift back to the high performance / cost choices. This might be an area where once you have chosen a service contractor you trust, go with their advice - but hold them accountable after the sale. The last word in this is also talk to someone who already has the system you are considering, word of mouth is the best marketing.

As far as the actual refrigeration system, keep in mind with any evaporative based cooling system (see split cycle above) if the temp cooling isn't called for at the stat, the compressor isn't running and there is no dehumidification. This is where region to region psychometric analysis needs to be done for proper system selection.

Desiccant dehumidification systems are very energy intensive.

The bottom line is residential humidity control (removal) is very difficult to do and architectural and exhaust fans use are in my book the best way to address it, not at the central system.

As far as heat pumps, ground coupled closed loop are the ones I'm familiar with, what ever system you go with pay close attention to qualifications and references of the service contractor, and again talk to folks with installed systems for independent reference.

I'm not a fan of paying extra for un-needed bells and whistles, yet paying a fair price for a modern energy efficient system is goal for all of us. That balance is of course the tough part.

The links I provide in my post's are all excellent research resources, if you want additional let me know.

One last thing to consider is mold, it can be a serious issue as Mole333 indicates. Many times mold is an architectural issue with poor vapor barriers, and infiltration via windows doors and other envelope issues. Secondary internal moisture loads are easily mitigated with proper use of exhaust fans in the bathroom and kitchen.

When I speak in the post about grid issues with humidity control I'm speaking primarily to commercial structures where code mandates a certain minimum quantity of outdoor air brought in for IAQ ventilation purposes - in other words CO2 and other contaminant control (CO2 is a common IAQ contaminant that comes from human respiration).

ASHRAE standards are the best resource to understand this, but the point is that current conditions are taxing the electric grid, and none of the politician or environmental lobby CO2 conversation is going to have any positive impact for easily hundreds of years as far as I'm concerned, so we need to sharpen our pencils and begin to think about modernizing our generating capacity like a national emergency starting now. The only two feasible ways to generate large quantity megawatts are via traditional fossil fuel and nuclear. As the heat is rising in the major AC regions now, as our grid is pretty much in the process of collapsing now, as our plants are all significantly aged now, the CO2 politics may be the least thing we should be worried about.

(coreection added, many plants are aged now)

Absent a stable grid, we could easily see European style problems with our aged population if we fail to maintain our AC.

I'm not in the marketing side of the business so I have nothing to gain by pushing this issue. Actually I'm the guy folks call when things go wrong, I wouldn't mind if the phone rang less often.