InfiniteClouds: GOG's entire colection of the Heroes games are on sale right now for $23.04. I did see that they are a different genre - turn based strategy... with RPG elements? I'm not sure what other games I would compare them to but they seem to be very highly regarded.
Ah! It didn't even register with me that they are currently on sale, since I already have them.
In a very broad sense, you will use heroes to move around the adventure map, collecting things lying on the ground, claiming structures to provide resources or other benefits to you, and fighting opponents. The heroes can level up, becoming stronger and better able to support their side in various ways (the biggest way is by better supporting their creatures in combat). In each HoMM, a hero always travels with an army (and only heroes can move around the adventure map), and the army does the actual fighting and dying in combat; HoMM4 is the exception, and the different role of heroes (as units on the battlefield) is part of what turned people off of it.
It has similarities to Age of Wonders, Warlords (not the Battlecry spin off), Master of Magic, Civilization, and Master of Orion. Some of these games are more similar (AoW), and some are less similar (Civ).
Heroes Chronicles is basically a set of extra campaigns for Heroes 3. You don't need one to play the other, but the engine and mechanics in Chronicles are straight HoMM3.