Do you know how to make an full adder with logic gates? Addition would be the easiest thing to create.
Well, WWLD could be nice - I myself haven't personally worked with it - but indeed even if you made an entire computer out of it you wouldn't want your players/viewers waiting for five to ten minutes for it to complete a complex task plus it might lag due to the required size to do any meaningful calculations. As a start it may help one with understanding the logic but there are also other technologies like NSCN/PSCN/PCTC/NTCT logic, SWITCH/ARAY logic, applications using CRAY, DRAY and all kinds electronics and the more advanced and fastest FILT/ARAY logic, each I'd be happy to explain as needed.
Also, are you planning to have the calculator run in decimal or binary? Plus, do you want to make a system that simply uses TPT logic and 'gimmicks' to perform simple arithmetic calculations or is your goal to eventually make a complex system that behaves a little more like a 'real' calculator (like a small computing system specialized for making calculations). Indeed there is a long way to go in learning from binary to boolean logic, full adders and robust input/output circuitry, but it will all be worth it whether you want to understand just how a calculator works, or even a computer.
Good luck.