The poor man's in home sleep study is pretty simple:

https://news.ycombinator.com/item?id=2030427

https://news.ycombinator.com/item?id=18465509

https://www.amazon.com/CMS50D-Plus-24-hour-Uploaded-Computer...

This is where things get really complicated. The output data of these tests are typically for a specialist to interpret, I'm not aware of "consumer" tests that break down things like "here's here you flipped over to your side" and "this is when you woke up". Specialists can interpret this, and can read past how you might adjust results yourself.

What gets covered by insurance and what doesn't is specific to your situation (what state/country you live in, etc). I just requested it with my primary care physician, who set up the consultation with a sleep center. Because my case isn't considered "problematic", it really helped to have a specialist request the CPAP, because otherwise, I'm pretty sure insurance wouldn't foot the bill. (I might add this is insane, because I'm sure I've added years to my life with the improved sleep. That's healthcare in the US for you.)

My impression is that the kind of tests is up to the sleep specialist to kind of figure out. The take home thing is much cheaper so I think they'll probably go that route first. I do note that they deal with a wide array of problems, like narcolepsy, sleep walking, night terrors, etc., and that's where I think you'll end up in a monitored hotel room.

Your local sleep doctor can evaluate your sleep apnea risk factors and prescribe a take-home test. Should be covered under insurance.

I think you can DIY with a cheap pulse oximeter, but I'm certainly not qualified to say how to interpret the results.