Following the child's lead is indeed ideal. I'd personally not worry about memorization versus critical thinking skills. My youngest is about the same age as yours, and both my boys memorize well. Memorization allows your child to learn fast and make connections, which is the basis for those upper level thinking skills.
For example, my oldest was and still is a sight reader. Once he started reading too many words to memorize, he would memorize parts of words and use that to figure out new words. For example, he never learned about hard versus soft c. He memorized words like "ice" and just extrapolated.
Here are some things my three-year-old enjoys: I see Sam readers (free online), all sorts of games (dice games, card games, bingo type games, etc.), mazes, puzzles, learning about time (calendars and clocks), and typing words into the computer.
In my experience, "progression" can be jumpy with little ones, so playing to interests is easiest and most fun. I'll add as well that my oldest was so far ahead that his fine motor skills turned out to be a limiting factor at a certain point; as a result, I've put a lot more emphasis on fine motor with my youngest to avoid/minimize that.
