Thank you for your interest in our laser cutting. It is difficult to get tight fits using laser-cut plastic since plastic sheet thicknesses can vary by + or - 10% (not only from sheet to sheet, but even within the same sheet). If you are not too picky about the fit, this might help:
Below are the nominal plastic thicknesses and their corresponding actual thicknesses. (Suppliers such as mcmaster.com do have plastic sheets available with actual thicknesses in inches, but we do not stock any.)
Nominal acrylic or ABS thickness, actual thickness
1/16", 1.5 mm (~ 0.06") + or - 10%
1/8", 3 mm (~ 0.118") + or - 10%
3/16", 4.5 mm (~ 0.177") + or - 10%
1/4", 6 mm (~ 0.236") + or - 10%
3/8", 9 mm (~ 0.354") + or - 10%
1/2", 12 mm (~ 0.472") + or - 10%
You are correct that it is more accurate to use the actual dimensions in millimeters. Note that the laser cuts down the center of the lines you draw and removes some material from either side of the line, so holes will be slightly larger than what you draw, and the parts that fall out of holes will be slightly smaller than the drawn dimensions. For laser-cut acrylic or ABS parts, relative to your drawing, your parts will be larger or smaller in diameter by about the laser beam thickness of around 0.005" - 0.01". The kerf is bigger for other materials that burn or melt more, such as rubbers, foams, and nylon.
If you want to ensure that a tab fits inside a slot, you could make the slot thickness be in the upper-end of the plastic thickness range of the tab. With the kerf of at least about 0.005", that would probably ensure the slot is wide enough. To be extra sure, you could try adding 15% to the plastic thickness instead of 10% (maybe even more if you want to leave space for some glue). For the other dimension, if you make the male and female parts the same length in the drawing, the kerf will ensure that those sides will fit together.
Acrylic is generally cheaper to cut than ABS (and less smelly; ABS parts might need to get aired out for a few days), so if you do not need the parts to be particularly sturdy, you might consider using acrylic. You can learn more about the two plastics at pololu.com/docs/0J24/3#abs.
I hope this helps!