I've been building geiger counters as a hobby for the past couple of years. I was consulting with some people in Japan right after Fukishima helping to build reliable detectors.
Geiger Muller tubes require a specific "plateau" of voltage to get consistent results. Too low and you're not picking up much radiation, too high and you get spurious results and can burn out the tube. The correct voltage varies with individual tubes.
This isn't normally a problem, except that there's a glut of surplus Russian geiger tubes on the market right now with unknown provenance and unknown parameters. Unless you calibrate each tube to find the plateau voltage, and unless you calibrate the resulting counter with a known source, the data you get will have no predictive value.
It's straightforward for a hobbyist to put together a project using one of these tubes and get it to click in the presence of radiation, and this makes a fine project for electronics learning, but you have to take further steps to get a reliable instrument. No one ever does this. The circuits I've seen have an unregulated high-voltage proportional to the battery voltage - it gets lower over time as the battery runs down. The voltage is chosen from the tube spec sheet, instead of determining the correct voltage for the tube. Circuits have design flaws such as using zener diodes for regulation, but not allowing enough current through the diode for proper function. And so on.
I've seen lots of these hobbyist projects in the past few years, especially since Fukishima. They're fine projects and well-intentioned, but generally not of any practical use.
Does radiation detection(with actual accuracy, linearity, and repeatability, not just a quick demonstration that you can add some noise to a webcam by pointing a small sealed source at it) have currently good, or at least promising for the not too distant future, solid state options?
Virtually any semiconductor will detect radiation. What you want is a semiconductor with a large capture aperture(*), which is the area through which the radiation passes. A 2n2222 transistor will detect radiation quite well, but it's capture area is tiny and won't see much of the radiation (saw the top off of a metal-can version and use a charge amplifier).
Power transistors such as the 2n3055 have large silicon dies and therefore larger apertures - as much as a square centimeter - but this is also quite small for capture.
The modern equivalent is to use a big diode such as a PIN diode. These can be quite large, but also expensive for the hobbyist.
A GM tube has a capture area which is the cross sectional area of the tube. These can be made quite large; and as a result can be made quite sensitive to the amount of radiation flux in the area. Hobbyists can also make their own tubes with enormous capture areas - it's not very difficult.
Large diodes are available for detecting radiation, but a GM tube is simple and can be easily made with a very large capture aperture. Also, GM tube their capture efficiency (the percent of radiation that gets in which is is actually detected) can be higher than the diode solution.
(*) There's capture aperture and detection efficiency. GM tubes have an efficiency of about 10%, meaning that only 10% of the radiation that gets into the tube is detected. Diodes have similar efficiencies, depending on the photon energy and thickness of the silicon die.