The bigger issue is actually living on mars - as romantic as that idea is, human habitation on the surface is really dumb, the radiation level is not insignificant, so anything long term would either have to be shielded or be under ground. And if we are going to build an underground colony....then why not start with one here on Earth?
If regular travel becomes a reality, you wouldn't shield the launch vehicle, but the cycler[1].
You would accelerate a small vessel (like a crew dragon or orion), intercept and dock with the much larger cycler, then enter the ship for your x-month trip.
When you near mars, you get back into your dragon, and burn away from the cycler, entering into martian approach.
7 people in a Crew Dragon for 18-24 months would not be pleasant. 7 people in a flying space hotel would be far nicer.
You could presumably look at using a small asteroid to provide the bulk of the "cycler", offering plenty of shielding for the trip, you'd only have to get it into position once - far less fuel requirement.
My understanding though is Musk is planning on using BFR to go surface-to-surface, with maybe a refuel in earth orbit. I believe this is because of the amount of material that needs transporting to Mars for the first 20 years or so, and that mass can be used as useful shielding. Even if Mars becomes self sustaining and doesn't require a large amount of cargo:people ratio, I believe Musk is aiming for a much shorter transit time than 2 years.
Or maybe even something like, as some have suggested (not me!), Phobos:
http://enterprisemission.com/Phobos.html
Warning: it's kind of out there. At the very least, it's perhaps interesting as speculative sci-fi.
Not as crazy as claiming Phobos is an alien spaceship though, with highly places ESA sources due to announce it soon (article date 2010)
Because if an asteroid hits Earth or if the world superpowers decide to go full nuclear, the underground colony in Mars will survive (unless superpowers decide to nuke that from here as well...)
So the tradeoff would be risking a finite amount of human lives in the short term to reduce the risk of a total loss in the long term. I.e. over time it becomes fixed vs. fractional cost.