Most importantly, I can't remember the last time I used my legs to browse the internet. I can see how typing with your toes would take quite a while, but old fashioned finger typing "humans + radiation" into google will be pretty quick.
Alphas die fast. They usually are so low energy that in air they only travel a few centimeters before losing most of their energy. In space then, your aluminum shielding will do you fine.
Betas are a similar story. Your spaceship will shield you fine from that.
Gamma rays will fly right on through, probably through you too, without depositing their energy in you, altering your DNA and giving you cancer, but there is enough cause to be wary. Blocking gamma's goes like this: 1.) Get as far away from the source as possible. It's energy falls off like 1/r^2. 2.) Stick high-Z, high density materials in front, which you can't really do in space because high-Z, high-density materials weigh a lot, so good luck getting it up there.
So basically, until someone perfects plasma shielding on such a large scale, we are out of luck. On earth though, we could all live in lead domes...kind of the anti-bio-dome. anyone remember that movie? lol.