You can’t go wrong with any of them, as they are all a bit unique in their own way.
Overarching timer forcing you to work somewhat efficiently to complete the game. Puzzles and difficulty are definitely the easiest in the series, but still provide a fun challenge to newcomers and veterans alike
No overarching timer allowing for a more laid back approach to completing. Introduces a 2nd captain and much more challenging/replayable end game content (a lot of people hold P2 in very high regards, and consider the end game content to be the most difficult in the series)
Technically there is an overarching timer, but it’s implemented in such a way that doesn’t create as much stress or pressure like the timer from P1 does. Introduces multiple captains that add another layer of complexity to puzzles as well as optimizing your daily efficiency. Has a very helpful world map that shows the location of objectives, captains, and loose Pikmin. The Deluxe edition has a slew of additional content that I haven’t even fully completed, but I believe they’re “prequel” missions that help to explain some of the events that happen before the start of the game.
You can’t go wrong with any of them, as they are all a bit unique in their own way.