Really really dumb question about heating and cooling systemsa

This might not be the right place for this but I suppose we shall see

Can someone please ELI5 heating and cooling systems please? What should I be looking for? What should I be hoping for? Is one type of system going to cause huge problems or cost more in the long run? My fiance cares a lot about our AC system. If it's not any good, he'll probably melt into a puddle.

Whenever I look it up online, I feel so confused.

For example, I'm looking at a property listing that said electric/heat pump and I'm thought those were two TOTALLY different things. It also has a fireplace??