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The EconoSplurge set is a fine place to begin from.
http://www.chessvariants.org/crafts.dir/econosplurge.html

Chess Variant Construction Set, a more sophisticated way to do it.
http://www.chessvariants.org/crafts.dir/construction-set.html

Both these sets are capable of adapting to different chess variants, due
to their fractured nature. Combining the set from the first with a wooden
board from the second would make a great set.

However, the second doesn't easily adapt to shifting board variants, and
variants that require an uncheckered board, like Shatranj, Shogi and
XiangQi, which is quite a board of its own, ('require' is a strong word,
but this is really part of the game;) and yes, 3D pieces.

For the pieces, I would suggest having two sets : 3D and 2D . The shapes,
all of them, should be vague, so they can be interpreted as the designer
likes.