You don't have to complete all the puzzles each day - unless you really want to!
You can browse the Special Issues section, use the "Search for Puzzles" feature in the Calendar View, or choose specific Suggestions prompts if you would prefer to focus on specific types of puzzle.
We do however recommend trying every type of puzzle in the game at least once, even if you aren't familiar with them - you can bring up instructions for any of the puzzles at any time.