You can't create a list of casual games without adding Sudoku here. And that's for a very good reason. Sudoku is designed to help you experience extraordinary puzzle games done fast and easy. You will see that many Sudoku boards are super simple, others are more challenging and interesting. The complexity of each board will mostly dictate just how fun the game can be or how demanding that can become as you go along.
Thankfully, there are a plethora of Sudoku games online, so finding the right one is not going to be that hard. It does take a little bit of getting used to if you want to get good at it, but for the most part, this is one of the nicer game types out there, and you will enjoy it immensely if you play it right. Just remember, the rules are simple, and they never change. While it will take a bit to learn the rules, once you do that you are good to go.