You can do it, you just need to be careful to protect your parts against static discharge. Be certain to touch the frame of your case frequently while pulling your parts out.
In terms of storage, you will need anti-static bags. If you have the ones the components originally came in, they should suffice assuming of course they are in good shape (one end neatly cut off, no holes, etc.) To be honest tho, I would pull the parts out, blow the dust off, and put them right back in. Your case is really the safest place for them.