Earlier today I saw this posted question in a group on FB:

"Hey everyone. New member, just getting back into photography after a long several year break. I'm trying to figure out how to select the appropriate camera profile in lightroom classic. Under the camera calibration section I select profile, but I don't have the profile for my camera. I checked in the application support folder and the profile exists, so I don't know what else to do. I'm looking for the nikon D3 profile."

It prompted this response that I thought others might be interested in. (I've edited the response to include further details and explanation.)

Sadly, I cannot answer the specific question regarding this person's specific camera, but it's worth looking at this section of the develop module.

Process Version

I've, frankly, not paid much attention to the Camera Calibration section in Lr, except to be sure I'm using the current Process Version. Lr defaults to the current Process Version, at the time of import. If you have images imported during the days of Process Version 3, e.g., your develop tools will be limited to what was available at that time. Change the Version to the latest and you'll be able to use the current set of develop tools. Do keep in mind that if you've already edited an image, and like the result, you may want to make a virtual copy to work on, as changing the Process Version will sometimes change the way the image looks.

Profile

Lr seems to default to Adobe Standard Profile, unless you have changed that in your import preset. I only recently became aware of the real differences available in the Profiles, so, I'm interpreting here. There is the default Adobe Standard, and all the profiles available from your camera. Caveat: I've also read that these profiles do not come directly from the camera, or even the manufacturer, but from 3rd party providers to Adobe. I can't confirm which is actually the case. But, in looking at the various profiles provided with the importation of images from different cameras, I do see a marked difference among some of them and the Adobe Standard Profile. It's someone's version of what the image would look like if you shot JPG and set your camera's Picture Style (Canon menu). The RAW image, of course, is just that, and changes are only applied once it enters Lr.

Here is a RAW image rendered in Adobe Standard:

Same RAW image rendered in Camera Landscape:

Camera Portrait:

Camera Standard:

And Camera Vivid:

The differences are subtle for the Canon choices. Other cameras offer other choices. A Fujifilm X-T2 will offer 14 Profile choices, including 8 monochrome versions.

And finally, if the Profile says "Embedded", you can't change it, it's baked in. That happens after the file has been edited outside of Lr and saved with a Profile, such as sRGB, AdobeRGB, etc.

The truth, as I see it, there is no "right" choice. You pick a Profile you like and use it as a starting point for your own editing. There's more than one way to get to where you want to be. This is just part of the journey, if you choose to use it.