Personally, I thing ignorant people *should* be learning about and experimenting with radiation detection equipment. The lack of understanding causes a huge amount of trouble, and this is how people learn. And telling people that they are too uneducated to ever understand this stuff is exactly why the public refuses to trust us when we say that they don't need to worry about Fukishema unless they are next door.
What they need to be told at the same time they start to measure radiation is Don't Panic. The governments radiation monitoring is very very conservative. If the government panics you might consider being a tad concerned. Yea, a few people will still panic - but you won't stop them no matter what you tell them. And the rest will actually start learning about this stuff.
So, in answer to this ask slashdot:
1) Unless the the reactor explodes yet again (and 10x larger than last time), don't worry. Your child will be in far more danger from more mundane problems, like cars, falling out a window, pollution, and electricity - and you can do something about those problems. They are more likely to drown in the clogged gutter than get irradiated by it. But when they are a little older they should love playing in it.
2) There are not consumer radiation detectors like there are smoke alarms. Unless you work at a reactor, you are normally worried about small leaks with long term exposure. Professionally, those are normally measured by
dosimeters. If you ever work at a facility like Los Alamos National Lab, you will have to wear one. You probably could get one to monitor your child, but the money would be better spend mitigating other, more serious, risks - or invest it today and it will help pay for their college...
3) Low cost hand held radiation detectors that give a live readout should be available from educational scientific supply stores. As others have noted, they are not all that accurate, and you really should not panic without a sold understanding of what is going on. But my high school class had fun when the teacher handed them out. Shortly thereafter the students found the uranium ore that he had stashed in a storage cabinet.
4) Understanding the risks with radiation does take a lot of research. You need to get a good idea of atomic chemistry. Just a few things you need to understand are the different types of radiation (electro-magnetic, alpha, beta, gamma, neutron, etc), what damage each type does, ionizing radiation, how it does biologic damage, and the ability of your body to repair damage. One thing to look into is how radiation danger is often evaluated based on the Linear No Threshold Model, and how that hypothesis is strongly disputed for low levels (in my non-expert view, disproved).
5) Sources: you can start by checking Wikipedia and google, but as you know they are not always accurate - and they are prone to getting overrun by alarmists. I don't know how much the Wikipeida editors actually know about radiation, vs just think they now.
One source I like is Enginering Disasters: Lessons to be Learned, by Don Lawson. He has several chapters on radiation, along with a good discussion of the Linear No Threshold Model. Some of his points are not as well supported as I would like, but still worth considering.
Another source to consider is entry level collage physics text books. Some of them should cover the basics of nuclear chemistry and radiation. For this topic, previous editions are very cheap and just as good (or better) as long as they were published within the past 30-40 years.