You get correction settings for vignetting by first photographing a perfectly flat, perfectly evenly lighted surface. Some use the north sky on a clear day.
In ACR go to the Lens Correction tab which is the picture of the cutaway lenses. Adjust the Amount and Midpoint sliders until when you run the cursor from corner to corner, the RGB numbers displayed by ACR change the least, or not at all. Hint...for my old Nikon D2X APS sensor, Amount was almost always 12, and Midpoint 0. For fullframe sensors expect larger numbers. It just might be the case that the best vignetting numbers are where the Midpoint slider has the smallest possible number that works.
On to Chromatic. Pick a raw file shot on a contrasty day with lots of contrast or texture near the corners. If you can find a disgusting white cigarette butt near the edge of the image, that's almost the perfect Chromatic Aberration target. Note that you will probably see red or cyan halos around bright objects. Adjust the Fix Red/Cyan Fringe slider to minimize the halos, noting that you can shift the halo from one side to the other. Balance out the Red and Cyan halos as best you can. Then go on to Fix Blue/Yello Fringe the same way. Check some areas more towards the center as well, you may have to compromise slightly between best correction on the edge and midpoints. Hint...for my wackiest wide angle its -28 or Red/Cyan, and -20 on Blue/Yellow. But my hyper-wonderful 55 Micro needs no adjustment.
Camera Profiles is a whole other thing, but lacking a specific profile for you camera just pick "Camera Standard" instead of the default "Adobe Standard." It's really a matter of taste, "Camera Standard" is prettier and I like pretty things.
LOTS of correction is possible in ACR. And since you are working as close to the original camera data as possible, you will do the least damage to image quality by making your big changes here, rather than later on when the data has already been scrambled a bit by RAW to TIF conversion.
Now the thing with panos is, you are covering very wide angles of view and one side of the image is almost always going to be brighter than the other. So I just load all the pano panels in ACR, pick one towards the center, get my basic "look" down, then work out towards either edge fudging the controls around to more or less make the outlying panels play nice with the look of the central panel, but without clipping. This means every panel may wind up having the different values.
For instance on Exposure, the central panel may be "0.0", but moving towards the brightest side of the image I have brightnesses of -0.1, -0.2, -0.2, -0.25, -0.3...that kind of stuff. For a newbie, just get that central image balanced, copy those settings to all the panels, then start moving out towards the sides trying to concentrate mostly only on Exposure. When the exposures on all the panels looks about as good as you can get it, then you can go back and mess with the other settings. An important concept is to make sure that as you adjust any of the sliders, that adjustment probably wants to "trend into" the same setting for the adjacent panels.
When evening things outs, it is helpful to watch how the histogram animates as you flip from panel to panel. Rather than making huge morphs, it's change should subtly change when going between adjacent panels (unless the actual contents of adjacent panels changes radically). Helps give you an idea how you're doing. Also ACR displays RGB values, it is helpful to compare the RGB values of pieces of sky that will overlap in adjacent channels.
Or you can just forget the last few paragraphs and shoot all your panos facing north at noon.
OK, so there you are. Gotta coat some prints.