The first purchase I made went totally wrong with the board size because I had no idea and simply relied on the seller’s recommendation. Since then I tried some online explanations (mostly quite unclear) and just seeing a lot of pictures. Correct me if I am wrong but I think most FIDE tournaments go with 3.75 inch kings and 2.25 square boards. But you may want to buy other sizes or you may not like the FIDE proportion.
After getting my own boards in most all sizes it got easier and just put pieces and boards together as it pleased the eyes most. When proportions are off it can still look ok, but it gets very hard to play chess and see clearly what is going on. Either when board too large or too small. Even very small differences can get quite disturbing for the eye. For example without the pieces I think no one can distinguish between a board with 2.25 squares or 2.375 squares. But some 4 inch king pieces can go on either, and some really can’t (for my eyes).
As I just discovered not all 4 inch sets are the same (at all), so a certain King size fits a certain square size is also not reliable. This goes for all the other king sizes as well I assume.
More important than how tall a king is, is how much space a set takes on a board. So I came to the following formula: length of 8 squares divided by the length of the 8 offficers (king, queen, bishops, knights and rooks tightly lined up.
So my Marshall’s officers measuring 12.57 inch go well on a 2.25 square board of 18 inch length. 18/12.57 = 1.43 which is for me the best looking quotient. So the fields are 1.43 times larger than the pieces. Anything larger than 1.5 is drowning the pieces in space too much. Smaller than 1.35 is too tight. For me.
All you need to know is the number that suits you best. Takes some time and can not be done (imho) with online photo’s. After that, when buying a new set I think it is not too much to ask of a seller how much 8 officers measure standing all together.