The different chess board sizes
When you are selecting a chess board and chess pieces a guideline you can use set forth by the U.S. Chess Federation’s Rules of Chess is the 78% rule which states:
The King should take up 78% of your chess board square, you can divide the base diameter of your King by 0.78 and viola you have the proper size.
Realize this is a guideline the chess police are not going to show up at your door and seize your set!
Common sense would dictate that the chess piece should not hang over the edge of the squares on your board.
Ideally there should not be large amounts of empty space around the base of the pieces either.
All said and done having the proper size chessmen that fit a board ideally is not going to make you a better chess player, it will certainly make playing the game more enjoyable, because you will have the proper spacing on your board.