I would not recommend 35mm squares as the offer for pieces will be very limited. 40mm squares can be nice but you need to find pieces around 2.8" size, they are not that common. Choice gets larger with 45mm squares and 3" size pieces (a nice example here)
Piece suggestions for 35 mm and 45 mm square sizes

Ohh I know the difficulties in finding pieces for 35mm squares. The reason for this consideration are:
1) I want a board that will fit easily on my desk
2) The Chessnut Air uses uses 35mm squares and I would like to modify a set or two with the sensors.

I don't agree with previous poster, I think 3" pieces are too small for 45mm square board.
I have pieces King size around 70-75mm [2.75"-3"] (diameter around 30-31mm) fitting very well on a 39-40mm square board. They are great as an analysis set.
Next square size is 45-47mm up to 50mm, which is good for casual play and bigger wood or plastic pieces with king height up to 90-99mm and diameter around 35-38mm.
3.3 The side of the square should measure 5-6 cm. Four pawns should fit on one square.
https://handbook.fide.com/chapter/StandardsOfChessEquipment2022

3.3 The side of the square should measure 5-6 cm. Four pawns should fit on one square.
https://handbook.fide.com/chapter/StandardsOfChessEquipment2022
FIDE doesn't follow it's own rule. Acceptable sizes are anything between 2 and 4 pawns fitting within a square, and it depends on personal preferences. Majority of world players don't prefer 4 pawns fitting a square.

3.3 The side of the square should measure 5-6 cm. Four pawns should fit on one square.
https://handbook.fide.com/chapter/StandardsOfChessEquipment2022
I'm leaning towards Chestnut Air which is square size of 35 mm.
The FIDE guidelines are for tournament sets. A board with square size of 35 mm is not FIDE. Nonetheless, ratio's are still relevant. I think 2 pawns diagonally on a square is acceptable. For a small board like this, I don't know what ratio's are practical.
Here's a Staunton set from CB. King height of 66 mm (2.6") and base of 32 mm. Pawn base is 23 mm. https://www.chessbazaar.com/the-collector-series-wooden-staunton-chess-pieces-in-sheesham-box-wood-2-6-king.html
A German knight Staunton set. King height 70 mm (2.75") and base of 29 mm. https://thechessstore.com/german-knight-staunton-chess-set-with-golden-rosewood-boxwood-pieces-2-75-king/
A French Lardy Staunton set. King height 70 mm (2.75") and base of 32 mm. https://thechessstore.com/french-lardy-staunton-chess-set-with-golden-rosewood-boxwood-pieces-2-75-king/

Chess Set Sizing - Pieces vs Board...
The primary sizing criteria for the pieces vs board is that of square size vs King base diameter...
A good rule of thumb is...
King base diameter = 0.75 * square size
or equivalently....
Square size = 1.33 * King base diameter
Any variation from these ratios, or the size of individual pieces and pawns, becomes a matter of personal preference...
https://blog.chesshouse.com/how-to-select-the-right-size-chessboard-for-pieces/
See also...
https://www.chess.com/forum/view/chess-equipment/a-system-for-sizing-chess-pieces-and-boards-long
You might also want to consult the FIDE Manual, Sections 2 and 3 on equipment regulations...
https://www.fide.com/FIDE/handbook/Standards_of_Chess_Equipment_and_tournament_venue.pdf
I have many tournament style chess sets suitable for a board with 55mm square. I would like to get a smaller board and a few different sets but trying to decide on board and square size. Something I can add a few different sets of pieces to.
I haven't decided how small a board I want to go with yet. Any suggestions of pieces for 45 mm squares? 35mm squares? I prefer wooden pieces.