I think we could have the technology to travel to Mars, and set up a base, but you would need a significant investment which most countries (even in groups like ESA) aren't willing to make.
There is a potential issue with radiation during flight, and in essence what you would do is build enclaves in the spacecraft which would use as much mass as possible from the spacecraft itself, and additional localised shielding to protect the astronauts during a (relatively short) solar event. Having said that, you would still be likely to get a higher dose of radiation than is optimal, but so long as (i) you could live with a slightly higher risk of cancer and (ii) didn't want kids. The first is likely to not be that much of an issue, since people happily smoke cigarettes and similar all their lives, and that substantially increases the incidence of all sorts of nasty things and (ii) could be (sort of) dealt with by making donations into cryo-storage before you left or just get the breeding over with before the journey!
Of course, you would only be hit by a solar event if you were unlucky, most journeys would quite likely be solar radiation free (aside from the higher background rate, which you would need some shielding against).
On the surface of Mars, there is a belief (yet to be proven), that Mars's crustal magnetic field may cause very localised magnetospheres. If this is true, they could provide protection from solar events in much the same was as the Earth's magnetosphere does, but you would have to place you base in the right location. Mars doesn't have a global magnetic field, like the Earth, since it's internal core has cooled too much for a self-sustaining dynamo effect, but it does seem to have frozen in local magnetic fields, left over from when the planet did have a magnetic field geologically much earlier. These may or may not create protection from the solar wind, but that's one of the sort of things that future missions will seek to determine (and I'm involved with proposals to put magnetometers onto future missions for this sort of purpose).
Failing that, it's also possible that we could manufacture some sort of Marscrete out of Martian sourced materials, and use that to construct underground structures, buried under sufficient loose material that it would provide protection from radiation. Similar schemes have been proposed for the Moon, where I think we have a better idea of the geological composition, so are in a more suitable position to suggest manufacturing techniques for Mooncrete. Future missions are likely to determine the Martian geology such that usable recipes for Marscrete may well be developed.
I'd go on a one way trip, assuming that it could be demonstrated that there was support for continuous development, because you would need frequent resupply with additional materials, for quite a while, regardless of how useful the surface of Mars is for the supply of some elements. It will take time to develop and install the mining and manufacturing equipment that is likely to be needed to create a self sustaining colony, although some of the more bulky stuff (like building material) is likely to be solved more rapidly.
Having said that, they wouldn't want me, because of my medical needs, which itself would require a continuous supply, since drugs which I need for my survival are far too complex to generate in such an environment for a substantial period of time.
