α decay... 4He clusters penetrate the Coulomb barrier.

β decay: an excess neutron changes into a proton plus an electron plus an anti-electron neutrino, via the weak nuclear force, or an excess proton changes into a neutron, a positron (anti-electron) and electron neutrino.

Following either α or β decay, the resulting nucleus is generally in one of its excited states, and it has to de-excite to the ground state by emitting photons. Since nuclear energy levels are generally an MeV apart, these γ-ray photons have a million times the kinetic energy of a photon of visible light.

Unless you eat the radioactive material, the only emission from a radioactive nucleus that can reach you across space is the γ-ray photons!  Solid matter is almost completely transparent to them.

A millisievert (mSv) is defined as "the average accumulated natural background radiation dose to an individual for 1 year, exclusive of radon, in the United States." 1 mSv is the dose produced by exposure to 1 milligray (mG) of radiation.  Americans actually get about 3.2 mSv per year from all sources.