Mars is hot

Radioactive that is.  Actually it's not uranium or thorium in the red sands of Mars, its cosmic radiation from deep space.  On Earth the magnetic field and the atmosphere shields us from it.  Out in interplanetary space it's more intense.  Mars has no magnetic field, so cosmic radiation on the surface of Mars is as bad as it is in space. 
  NASA using data from the Curiosity rover, found that astronauts on a 500 day round trip to Mars, would absorb a dose of one whole Sievert of radiation.  That's a lot.  A Sievert is a Euro unit invented in the 1980's and it's big.  One Sievert is 100 REM, the more usual US unit of radiation.  
   US safety standards call for not more than 5 REM per year for civilian workers.  NASA is more daring and permits the Shuttle astronauts to absorb 25 REM  in one shuttle trip.
   If memory serves, 300-400 REM is the 50% lethal dose, half the people exposed to that level of radiation die within weeks.  100 REM for a trip to Mars is scarily close.  NASA estimates that such a dose would increase the risk of cancer over a lifetime by 5%.  That sounds optimistic to me.
   However, I expect no shortage of volunteers to fly to Mars regardless of risk.  
   Shielding a space craft with lead probably does not work, the required shielding would weigh so much the space craft couldn't get off the ground.  An ingenious design might put the crew compartment in the middle, surrounded by the fuel tanks.  This might work on the way out, but on the way back with empty tanks, not so good.   Or the space craft might shield itself with a powerful magnetic field, created by neodymium super magnets, or a super conducting coil of wire.  The Earth's magnetic field isn't all that strong at the surface, but it is very deep.  My electromagnetic field theory is no longer strong enough to calculate  just how strong a magnet would be needed to give the same shielding effect as the Earth's field, but the number is computable.