Safety isn't a particular issue, but with anything close to current technology, "the Asteroid Belt" is a vast place to be commuting around-- it encircles the sun in an orbit wider than the Earth's, and traveling from one asteroid to another would in general be a long and expensive voyage. You'd probably focus on just one juicy asteroid, in which case it would make a lot of sense to live inside it (since you're excavating anyway); then you have good protection from both radiation and debris.
Of course, if the destination for the mined resources is Earth, there is a lot to be said for bringing the mountain to Mohammed as Rob Kinyon says-- either parking it in orbit or just (carefully) landing it in the ocean. No commercial enterprise is going to pay $6 million a year for someone to work a jackhammer if they don't have to, after all.
However, a major market for asteroid-mined materials would be other space construction projects, where anything shipped from Earth is hugely expensive because of launch costs. The economics of that market would favor extracting and refining minerals at the source, and launching them on a slow but super-efficient trajectory to their destination. So, you'd continually fire aluminum ingots out of a cannon on Ceres, expecting to sell them 20 years later when they show up orbiting Ganymede. It raises a lot of interesting narrative possibilities (e.g. people hijacking the material en route)...
