The cost would have been a few hundred million dollars if the Shuttle launch could have been begged from Congress. Without being able to launch a hydrogen fuelled rocket from the Shuttle, the mission becomes more complicated. An unmanned resupply launch would be required in two or three years assuming two people as the initial voyagers. Today there are other alternatives. One is to launch the unfuelled vehicle in the Shuttle and fuel it from Russian expendable launchers or from the Shuttle tank in low earth orbit.
Someone has to raise the money.
The amount for the one-way moon mission is within the capability of many single individuals. Good contacts and good publicity are requirements. The name comes from the following. Small wages, bitter cold, long months of complete darkness, constant danger, safe return doubtful. Honor and recognition in case of success.