Wax won't hide cup stains, but it will seal in dirt. Your best bet would have been to start by cleaning the woodwork. That requires something like Sugar Soap or possibly a furniture reviver. The problem is that you have now waxed the woodwork, sealing in the marks, etc - and the problem with wax is that it won't allow you to apply other finishes, or stains, or furniture revivers on top as ut seals the timber. This means you may now he reduced to trying to get the wax off with a hot, strong solution of washing soda in red hot water and a scrubbing brush; or an industrial solvent/petroleum distilate (naptha is the best, white spirits is less effective but easier to find); or a proprierary solvent such a Liberon Wax Finish Remover (expensive); or even industrial acetone; and clean, white rags before sanding it all down. Wear gloves. Work in a well ventilated room above ground level. No naked flames or smoking with the distillate solvents!
Only when the wax is gone can you consider stains and finishes
FYI the standard advice with finishing is always to try any technique out on a small, inconspicuous area before applying it willy-nilly