That's a great question, and can apply to all kinds of situations, characters with different outfits or weapons and many other things.
in your case, with just 3 colours, your total number and size of sprites will still be relatively quite small. So, it will come down to trading a slight memory improvement with a little more complicated code.
Since this is your first game, I would recommend keeping it simple and go with making the full tile set in each colour.
Although, there is a third option - make one set with the tile background white and black lettering, then use "Set Color to rgbEx(xxx,xxx,xxx)" to make the tile the colour you need. The background will change, but the lettering will stay black.