Good question. Most places (e.g. guinealynx ) recommend half a cup per piggy per day, but I've always thought it was rather odd to express it in volume rather than weight, because some veggies are almost all water and others contain more dry matter (i.e. nutrients and fibre).
As for variety, as long as your piggies are getting unlimited hay and good quality pellets, which have all the micronutrients they need, I don't think variety in veggies matters much from the health point of view. It does matter from the boredom point of view, though. We give them as much variety as we can manage.