Recommendation for Fan/Light switch

I’m running OpenHABian on a Raspberry Pi 3 and am enjoying how it works with my WeMo power switch, TP Mini HS105 switches and Philips Hue lights and bridge. It will start to get hot in Georgia soon, and I’ve been eyeing my overhead fan. The fan is an older style with a pull chain to control speed (off, high, medium, low) and lights. I have a wall receptacle with 3 toggle switches for fan, lights and a 3rd (I guess a power outlet). I picked up an Aeotec Z-Wave stick and loaded the Aeotec bindings in my OpenHABian Pi.

Any recommendations to move the fan and overhead light to something smart? Is the GE Z-Wave Ceiling Fan Wall Controller the way to go? Right now the lights in my fan don’t dim. Would I just buy a basic smart on/off switch for that? If I went with a dimmable smart switch and dimmable bulbs, would that give me dimmable lighting in my overhead fan, or should I just stick to simple on/off for fan lights and leave the dimming to my Philips Hue bulbs?

Are there better ways to go about this? My wall receptacle with on/off switch has 3 switches in it. Are smart switches significantly bigger, causing me concern for room to mount 3 smart switches in one receptacle?