Yeah, well I will probably stay on High Sierra. I'll try Catalina out before as I have a Catalina USB downloader/installer, but if preformance is not like that on High Sierra I'll just restore from a backup I have.
I've seen some running the original OS X like 10,6 Snow Leopard on old iMacs like mine that would go much higher. Some also use Mavericks. But it probably is better for me to go as high as possible, like High Sierra or Catalina, right?
I have an install disk for 10,6 so installing wouldn't be a problem.
What would any advantages be when using 10,6 or 10,9 instead of High Sierra? I do not have any software that I want to use that needs PowerPC or that is 32-bit.
10.6 is essentially unusable. No support for anything in 2022. It is blistering fast though!
10.9 is also essentially unusable IMO, but others may disagree. There are lots of workarounds to get things working, but IMO it's not worth the aggravation.
I used to say 10.11 was fairly usable, but it now has issues with SSL certificates, which can cause problems for surfing, even though the OS is supported by Chrome. Again, there are workarounds, but it's not an ideal situation. There are other compatibility issues with various software too, with some applications just not supporting 10.11 at all anymore.
10.13 High Sierra is very usable. It supports current versions of both Chrome and Firefox, and it supports the APFS file system and HEIC/HEIF file formats (which current iPhones and iPads use) as well as HEVC. Speed is very good on High Sierra. Numerous current features of OS X are still fully supported on High Sierra. This is what I use on my Core 2 Duo machines now, booting in HFS+ to keep the normal boot process with dosdude's patcher for 10.13, but it has APFS support for external drives if necessary. Most software out there seems to support 10.13, although there are exceptions, so it depends on what you are using, but most of the mainstream stuff is fine on 10.13.
10.15 Catalina can be very usable, but while I don't own that specific machine, I have found that on my Core 2 Duo machines, Catalina doesn't really feel like a fully legit Mac experience. You need hacks to boot APFS and there are various things that kinda make them feel like hackintoshes. Chrome was also buggy in my case on Catalina, on both those C2D Macs, but Chrome runs perfectly on High Sierra on the same machines. My C2D machines are lower clocked than yours though at 2.0 GHz and 2.26 GHz, and they feel a bit more sluggish on Catalina than on High Sierra. They are already sluggish on High Sierra of course but it's worse on Catalina. However, I think a 3.06 GHz C2D could feel relatively OK performance-wise on Catalina.
tl;dr:
The options to try are 10.13 High Sierra, 10.14 Mojave, or 10.15 Catalina, but I personally would recommend High Sierra unless there are some specific features or some specific software support you need in Mojave or Catalina.