How you deal with the settings depends on the display device itself and the software you are using.
Color luminance is not "the most important thing" - grayscale is "the most important thing" then color luminance, then color xy (or hue & saturation). But a big hue/saturation error can easily overcome a smaller color luminance error so it's a slippery slope to try to say one thing is more important than something else.
Using CalMAN, you'd ideally want all color luminances to be "0". If they can't all be made to be "0" (assuming you are using the color luminance bar graph where the bars can be negative or positive (above or below 0), the next best thing is to try to get them to all be the same (like all 5% above zero or all be 7% below 0) but if the best you can do is to have all of them WAY above or WAY below zero, that's going to look really bad and you're better off NOT making them all equal. A video processor can't make any color luminance brighter than the TV or projector can make it. So if you have one color that is, say, -30%, you essentially cannot fix that (unless it is caused by the "running out of gas" issue explained earlier). The only possible fix might be to try increasing the Color control or some other setting to see if the control happens to raise the lowest luminance problem high enough to get to "0" - without worrying about the other colors getting too bright. Once the lowest color is up to "0" you can reduce the luminance of the other colors in the TV/projector and if you can't fix all of that in the TV/projector, you still have the video processor for final adjustments. The function of controls varies from one model to the next so you always have to check to see if something like raising the Color control helps -- in some cases it won't do anything helpful OR it might help luminance but create other problems so you might have to balance the "fixed" problems with the "worsened" problems so neither one is visible. All this stuff is why pro calibrators exist - it can seem overwhelming in the beginning.
Yes, you can use the gain/offset (or high/low or some other terms the display manufacturer might use) controls to improve gamma... if gamma is too low (i.e. 2.0) and you want it higher, 2.0 means everything between black and white is too bright (gamma does not change the black point or white point, it changes the shape of the curve connecting the black point to the white point). So you can darken red, green and blue using the gain/offset controls to raise the gamma number -- again these controls work differently from display to display so you might lower all of them the same amount in some displays while other displays may require different amounts of reducing the settings in questions.
When calibrating with a video processor, you want to calibrate the projector first avoiding huge adjustments to anything. If there's a HUGE error somewhere, you might want to fix half of it in the projector and the other half in the processor. The projector need not be "perfect" before going to the video processor, but you should eliminate problems so that the projector is reasonably OK before moving on to calibrate the video processor... and you want to start with the video processor being "reset" so it isn't changing anything before you begin measurements or adjustments. If the processor has previous settings in it, you can get confusing or conflicting measurements.