I'm looking for a good and reliable pulse oximeter for home use. What are some good brands and models you have used? If possible, I'd like one that does overnight logging (if it's not too expensive)

Going to watch this.

I've used pulse oxmeters but never for overnight logging. I couldn't imagine the one's I've seen and used would work when sleeping. I think they would all fall off or at least move enough to not get a reading. Unless you don't move at all when you sleep.

Maybe you could rent one if you only want to see results for a short time. See if your Doc will order overnight oximetry. I would think one that records, and/or prints out would be expensive to buy.
A good brand with a good rep is Nonin. I have a NoninGO2. IIRC, it was less than 100.00. Less now. There is a Bluetooth model for 229.00 on EBay. That way you could probably print results. Hospitals use NellCor or Puritan Bennett(?), Respironics, maybe others too. There are options on those models which allow the sensor to be taped to your finger to get continuous readings.
There are a lot of cheaper models out there. Priced about 40.00 or even less.
The thing to remember is that all PO (Pulse Oximeter) are +/-3% accurate. Even Hospital POs. But they got to be more accurate than a 40.00 MIC PO. Either that or they're wasting their money. You are looking for trends. And there is no way to calibrate them. So don't just jump and go with the first number you see. Change locations of PO, different fingers etc. different fingers have different circulations. Different POs give different readings. But it's the trend that you're looking for.
Gustover or someone else still working will be along shortly to give direction also.

I use the Mossimo with an iPhone. It works flawlessly but is pricey. It is right on with my doctor's and hospital's devices.

It will record up to 12 hours and has the ability to connect with cloud storage if you like. I use it stand alone with an app from the App Store.

It's available on Amazon and elsewhere.

For overnight, one of the stand alone devices or one of the Bluetooth devices may be easier to manage. The corded versions can get tangled/pulled.

Many years ago, I bought a stand alone for my now deceased father. It worked for him overnight but took an engineering degree to get the material to a printed form.

You may wish to investigate how easy it will be to review and print the overnight results before you buy a given device.

I have a Contec CMS60C color pulse oximeter that has worked quite well. It does everything you are looking for. Software initially was problematic but I "broke the code."

Contact this member, he's in the business. Link
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I may have a flux capacitor to sell............