Howevever, if you want something really portable, that can warn you of dangerous radiation levels, get a device called a NUKALERT. It is small enough to hang on a key chain (my wife keeps hers there; I keep mine in my pocket), and gives you a rough measure of radiation level. Good enough to tell whether "it's safe to go out yet."
Incidentally, building a GM counter isn't all that easy. I tried it when I was in high school, back in 1949. The electronic circuit isn't all that hard, not even with vacuum tubes. It's simply a trigger circuit that takes pulses from the GM tube and converts them into square waves. Building the GM tube itself is really difficult. My several efforts weren't good enough. Evacuating and sealing the tube is tough unless you have industrial-grade equipment.
I have one.