I'm trying to convert to electric because electricity is super cheap here, no trips to buy propane, no worries about running out in the middle of a brew session, and it's silent. Not saying one is better than the other, but electric is better for me and my situation. Electric is often a little more expensive to set up, and requires a fairly large circuit or circuits, which not everyone has. One advantage to propane is portability for things like group brew sessions.
HEX is an abreviation for heat exchanger, the central component to a HERMS, which is short for "Heat Exchanged Recirculating Mash System". It is typically a long coil of copper or SS often mounted inside the HLT. The water in the HLT can be heated and then the wort can be recirculated through the HEX to maintain or change mash temperatures. Some HERMS users fill the HLT with cold water or ice after the boil and pump the wort through the HEX so that it acts as a chiller or pre-chiller. There are a couple of examples of HERMS in the homebrewing wiki, and many others can be found by searching the DIY forum.
Whirlpooling is the act of getting the wort swirling around quickly at the end of the boil to let the hop particles and break material form into a cone in the center of the BK. The wort can then be drained or siphoned leaving all of the debris behind. The pump can be used to form the whirlpool. See here-
https://www.homebrewtalk.com/wiki/index.php/Whirlpooling
Automation often allows for more precise control of certain aspects of brewing, but is by no means a requirement. Being able to push a button and know that your complex step mash will hit all of it's temps and times perfectly would be nice, but I plan on a mostly manual system for myself.
Having tried both styles, I prefer batch sparging for its speed and simplicity, but it's just a personal preference, and many brewers swear by fly sparging methods.
I'd suggest reading all of the great build threads in the DIY section and the Wiki for some ideas, and to learn more about the various systems and options out there. Try to find someone nearby with a HERMS or RIMS who will let you see their system in action. Even watching someone brew an AG batch using a gravity fed cooler and keggle set up will help you figure out what you like and don't like in a brew system. Maybe start with a super basic system and brew a couple of batches before commiting to any specific upgrades. This would allow you to figure out what upgrades would work best for you.