Settlers is THE entry game into the world of strategy games. Anyone can enjoy it. The game is ever changing as the board is different every time. There are many expansions & variants to keep everyone interested. It's one of the best out there!
Agricola is a fantastic game for someone used to the complexity of strategy games. I love the 1 player feature where you can play a series of solo games against yourself. There is mostly strategy with a little bit of luck involved. This is fun solo, 2 player and 3+ player. It's addicting!