Ok, so I did some digging in my canon resources.
First I need to correct the IRE values I gave you earlier. Here is the exposure for 18% grey recommended by Canon, these values are indicated in this great paper for the C300mk2 but I saw similar values for the C200:
C-log 1 = 34% IRE
C-log 2 = 39% IRE
C-log 3 = 34% IRE
I think C-log 2 is only available by default when shooting Canon raw with the C200 but there is no C-log 2 for 8 bits recording on the C200 which makes sense considering how "aggressive" c-log 2 is. Personally, I have no shame to revert to non log curve on some cameras because shooting with aggressive log curve on many 8 bits cameras is a non-sense (eg. S-log 3 on sony, D-log on earlier 60mpbs 4k DJI drone, etc.). I see too many people selecting C-log no matter what because it's "Pro" or "better"... This is plain stupidity if you can't nail the exposure (eg. uncontrolled environment outside) or don't have advanced grading skills.
Don't forget that you can apply LUT directly to the LCD screen if you prefer to expose "visually" as judging exposure on the screen in Log can be tricky and it might be the reason why you underexposed in the first place. Indeed, on the screen, Log footage looks brighter which is why you should stick to a reference (grey card and IRE value, X value for certain type of skin-tone, or ballpark estimate on the EV indicator).
Also, as far as the colors and look goes, check the "Color Matrix" in the Custom picture/HDR menu (where you set the gamma). Here you must understand how it works with the C200. There are basically 2 options to select the gamma curve:
#1. Select one of the presets (Off, BT.709 (WDR), C-log, C-log 3), here the gamma curve and associated color matrix are grey out and they are locked inside the preset with these settings (screenshots from the C200 user manual)
#2. Leave preset OFF, then the gamma and color matrix are not grey out and you can choose the combination you want. Notice from the table above how C-log 3 uses the neutral color matrix whereas C-log 1 uses the "Cinema EOS Original" which is a color profile designed to match colors across the EOS camera board (eg. C100, C300, etc.). You may want to play with that if you are not satisfied with the color and overall rendering.
Finally, you can also tune the colors in the "other settings" option in the CP/HDR menu.
Cheers
