My favorite iterations from those two series were the 4th iterations, but I was introduced to them by their second iterations and played the the 3rd iterations quite a lot. I also have enjoyed The Sims, and my favorite iteration of it is The Sims 2. Haven't really bothered with 3 at all.
Age of Empires is a real-time strategy game. If you've played Starcraft, it kinda plays like that does, except with a more earthly setting. The original Age of Empires spans all of human history up to the time it was released (1996), Age of Empires II is set in medieval times and during the Renaissance, and Age of Empires III is set during the colonial era.