You have teacups!! And saucers?I feel humbled, I've only just upgraded my old plastic mugs to china ones. But it's still far easier to drink from a bottle.
The stains stay on the cup cos the water is hard and the calcium sortoff stick aroudn the edges. drips on a bit of Viakal (not too much needed really) from supermarket then rinse and washem. Same applies to non-sparkling sinks and bogs. Make sure any visitors clean the sodding cups properly!
Easy peasy. Buy some of that powdered Steredent stuff (the pink powder that people use for cleaning false teeth with) Fill up a bowl with warm water, mix in some pink powder, and stir. Drop in cups, teaspoons and anything else manky stained and leave to soak (overnight if v bad) Rinse. Perfect.