Here's a diagram displaying the penetrating power of different types of radiation.
But in all seriousness, your real concern is going to be ingesting radioactive particulate over simple radiation exposure. And anything you can do to prevent yourself from inhaling dust will help with that. Typical levels of radiation in an industrial setting are still relatively low even at a nuclear power plant. So basically, you'll probably be fine with just a geiger counter and a dust mask. Just make sure the counter doesn't go over 200 cpm. The most radioactive place I've ever been maxed out at around 180 and that was an abandoned uranium mine.