I thought that if we were going anywhere in the Solar system (which I really hope I can see in my lifetime but I doubt it) that it would be wrapped in a lot of mass. For example I thought ice first because it's water and we would be using it. So if we carry a-lot of water that is what we would be using as shielding. Either that or rocks we can gather up *in* space (maybe a lunar space elevator [a moonstalk iirc?]).
However for our first small ship and given that cosmic radiation may be a lot more energetic than I think and, given that it adds mass to the space craft then why not just go *inside* a big water tank, which would also be your water supply? At first using separate launches with water tanks, however later, maybe a small ice asteroid we capture with a robot and melt - or even carve into, could be a water supply.
Speaking about capturing asteroids maybe we can build a fast, nuclear powered robot ship to explore the asteroid belt remotely and leave robotic mission payloads on large asteroids whilst identifying resources. Maybe when it has built up enough speed we can send it out to the Oort cloud for a look around. I know it sounds science fiction but it is not too far outside our technological capabilities, and, if the world pooled resources to achieve it, something that might bring nations together for a common goal. I know, probably just a fantasy, but I am a geek.
Besides, all children have to start moving out of home sometime.