Personal private missions to mars and beyond (with near-future technologies) are only possible with additional aid on the way such as fuel refilling stations in space, resting places on moon/mars/asteroids etc. As for going out of the earths gravitational pull, I think the cheap and best way is to use the space elevators which will be coming by 2020 (though each launch into low-earth-orbits through the elevator themselves may take 2-3 days). Once in the earths orbit, fueling station in the orbit can be used for fueling the ship. Of course, fuel has to be put into orbit first.
Or you can use sails (similar to solar sails) powered by highly coherent laser beams produced by orbiting satellites for a considerable distance.
Fuel refueling stations are being made possible by companies such as planetary resources who mines asteroids for precious resources and water is the most precious fuel in space.