Can you recommend any games?

Dominion. The strategy arises from observing how the specific cards that are part of any given game interact with each other.

Agricola. There's a lot of "designed" complexity here too, but a good deal more arises, particularly when you look at planning the critical eight first actions, and the path to the first additional family member.

Neuroshima Hex! is a bit nerdy looking, but it's simple without expansions. Retro apocalyptic setting with mutants and evil robots. A knife fight in a telephone booth, plays well up to 4 players. You fill up the hexagonal board with your troops (they mostly don't move) rotating them so that they will hit the most enemies. Then it either fills up completely or one of players plays Battle token, and everything goes off like a chain reaction. Units hit in melee or shoot in order of their initiative. High interaction, tight mechanics. Most people prefer it as a duel game though. You can play it online too.

Tigris and Euphrates is an old classic that has very few tile types to place, but they result in complex outcomes. I can't say very much about it because I only played it once on a game show, but it's on my to-buy list.