This question comes to us all the time. The first thing to remember is that there are a lot of types of radiation. What are you looking for? You will never be able to detect everything in one instrument.
If you are looking to detect electromagnetic radiation from household wiring and appliances, you will want a gauss meter that is optimized for the electrical field frequency. In the U.S. this is 60 Hz (60 cycles per second). These are available from a variety of sources.
If you want something that measures radio frequency emissions from microwaves, cell phones, radio transmitters, fluorescent lamps, etc., you want a radio field strength meter. These are a little more complicated than a gauss meter calibrated for a fixed frequency. Radio frequency energy exists across a broad spectrum of frequencies from the ELF (extremely low frequency) band, all the way up VHF (very high frequency), UHF (ultra high frequency), and microwave frequencies. For a meter to be accurate it must be sensitive to the frequencies you are interested in, and have an appropriate antenna, if you are going to be able to get accurate measurements.
When the wavelength of electromagnetic radiation gets short enough, itʻs intensity and penetrating power increase to the point that it has the ability to ionize and change the structure of matter. When ionization takes place inside the human body, a variety of effects can occur. These range from the production of free radicals, which can cause inflammation and disease, to DNA damage (which can cause cancer and birth defects in extreme cases). For this type of radiation you need a geiger counter or something else designed specifically for detecting ionizing radiation.
There are also particulate forms of radiation that can ionize matter. When I say particulate, I mean like very tiny charged particles. Beta particles have mass and carry a negative electrical charge. Alpha particles have mass and carry a positive electrical charge. Alpha particles are believed to have 20 times the potential to cause damage within the human body, when compared to gamma or beta radiation. You need specialized equipment to detect all three of these forms of ionizing radiation. The most economical way to detect them is to get a geiger counter that has a mica window capable of detecting all three forms. The most powerful form of this detector is called a “2 inch Pancake” detector. Hereʻs an article that makes some important points about the good old “pancake.”