Beta particles are fast-moving electrons emitted by many radioactive elements. They are more penetrating than alpha particles, but easily shielded. They are very penetrating and require shielding. Radiation dose badges are worn by workers in exposed situations to detect them and hence monitor exposure. All of us receive about 0.5 - 1 mSv per year of gamma radiation from cosmic rays and from rocks, and in some places, much more.
Fast neutrons can be very destructive to human tissue.
The current maximum permissible dose to radiation workers is 20 mSv per year averaged over five years, with a maximum of 50 mSv in any one year. This is over and above background exposure, and excludes medical exposure. The natural background radiation is about 2 mSv. Such levels are achieved with straightforward techniques for ventilation coupled with rigorously enforced procedures for hygiene. The standards established by the Nuclear Regulatory Commission in the USA limit worker doses to no more than 50 mSv per year.