High energy gammas, electrons, and charged particles give off bremsstrahlung radiation when they are stopped- this means that you approach diminishing returns as you apply shielding against space radiation. Using twice the lead does not result in twice the shielding.
When you get away from Earth and you don't have Earth itself blocking half your sky and the mag field providing some geomagnetic shielding, space radiation levels go up. You don't have trapped protons, but you have more higher energy stuff.
This pushes you up against weight limits quickly. I'd imagine that you'd need many launches to assemble your Mars ship in orbit, with the living quarters inside a half-inch steel,aluminum, and lead case, surrounded by a foot of water (you recycle the water all the time to live off it).
There are solutions, but they are much more complex than the Apollo tin can or Ti-Al-ceramic of the Shuttle.
My first take of magnetic shielding is to think of Earth- our mag field funnels particles into the poles and traps e and p in the van Allen belts. A big coil around your ship would funnel particles too, and would not touch galactic cosmics because they are too energetic.
http://radiationshielding.nasa.gov/transport_calc1.html
Go to the above link, click on "go to transport calculations"- there is a quick and dirty calculator that allows you to see how shielding effectiveness drops off with increasing particle energy. The calculator uses an orbital particle flux that was measured during a flare. The thickness of your shield is not in inches, it's in g/cm2, so all elements are normalized to density.
So how come most of the larger life forms on this planet inconveniently (for this theory) fail to die off during periodic reversals of the Earth's magnetic field?