I did take a chance and tried a budget-meter from China, but it turned out to be a complete farce (didn't report any measurements at all), so I got a refund. For now the oxygen test project will go on hold. Maybe I can borrow or rent one from some lab for a few hours.
That aside, I also have wanted to acquire a quality/accurate geiger counter. I'd gotten an alpha/beta one many years ago, many house moves ago, and I don't know where it is. It was sort of an amateur level one, so I'm not that disappointed.
I did have a look online to see what's available now in something closer to a pro-level, and I found one that measures alpha, beta, gamma, and x-ray. And unlike the oxygen meter, this is something that could be useful in many situations, and last effectively forever (as long as I don't misplace it!).
It arrived today and I literally just spent a half hour with it doing a survey of my place. A few years ago I had done a Radon survey and it came up in the acceptable levels (.8 to .9) although most of the other places I have tested (previous homes and my workplace) were .4 to .6 ....but, still relatively acceptable by normal standards (below 2.0). If I get the gumption eventually, I might still see what the cost would be to hire a service to have it lowered even further, but it should still be fine either way (knock on wood).
Here's some more info on Radon:

and RADON PAGE .
The MEAT of this post though, is the reading I got from the Geiger Counter :>
Most of the place is in the normal range of radioactivity, backing up the findings of the radon test gauge.
However...
I did make a couple of discoveries.
A piece of my grandma's antique carved leaded glass is about double the radiation in the room. I checked another piece and it also seemed a bit elevated. This is most likely (essentially) harmless beta radiation.
But the MAIN shocker was that my grandparent's antique Clock is a VERY HIGH Emitter!! I had this on my desk for over 30 years!
Luckily it's likely to be alpha radiation, ... which is the most dangerous, only *IF* in close proximity for extended periods of time on average... less than 6 centimeters generally... and I was further from that distance when at my desk.
Still... I think I will box the thing up safely and store it out of the house :|
It's a pity, the thing is amazingly cool-looking, with hands that float in mid-air: 
eeesh....
I will continue testing things occasionally, but for now I think I've surveyed at least 95% of the place :}
And I might take the geiger counter with me to my dentist visit next time I get an x-ray :D
UPDATE: I have boxed it up and stored it centrally in an old metal freezer outside.
I had the Geiger running nearby as I boxed it up, and it was still giving off some unsettling readings, in the box, up to 2 feet away. arrgh.
I took readings from outside the metal freezer bin, and it appears to be completely shielding the contents. Yay!
Once in a while, if I have to open that non-working freezer to access some other items stored inside there, I'll just be sure not to dally too long.
The big picture though, is that this thing has been in and about family houses and storage for probably 75 or so years, thus the plan going forward is just to respect it and give it the space/perimeter it needs to be safe-r ^v^
eeeeeeeeeesh!