DarkMirror

As title says, I've heard some conflicting things regarding performance in these modes. Some say that Sport mode is actually faster than Manual and the ESP sport nanny is slightly more efficient than completely off especially when modified since the low end torque is so high and causes wheel spin since our rears tires don't really get much bigger than 275 without going wide body. Maybe it's different depending if it's pre-facelift or not due to the MCT?

I'm not a particularly skilled driver so it doesn't matter much personally, but this is the kind of stuff that keeps me up at night.

Birdseye

Sport mode isn't the same thing as Manual mode at least on a Facelift model. There are 3 different traction modes at least on my facelift model, all of which increase the amount of slip allowed. The 'stock' mode as you turn it on will still let you do some silly tail happy still compared to other cars, just as long as you don't mash the throttle suddenly then the traction control kicks in. Sport mode allows for more aggressive quick throttles that will let you crash the car/have more fun. Turning ESP "off" does not actually turn it fully off, but it does let you get more wild than sport. I run stock if it's raining or very cold, Sport much of the time, and "ESP off" if it's a nice warm day on a backroad and I'm at my full capabilities. Perhaps I'm being a bit conservative, but tuned to 540hp this thing LOVES to go tail happy even in 'stock' mode.

Generally I think you can crank up the slip as conditions improve. If it's cold, don't risk it... as it warms up you can play more. I don't worry too much about what is fastest unless you're hitting the track, a lot of the joy of the C63 is just the tail happy V8 nature, just you and throttle steering an absolutely insane-sounding engine. I just don't want to crash, others are more risky.

tphss

For the setting questions, I have a similar car to yours, pre-facelift. For the transmission, basically the case on most older generation Mercedes vehicles is that the transmission on S (Sport) automatic yields the 'quickest' shifts.
C (Comfort) is the smoothest, lower shift points, and starts from 2nd gear on standstill.
S (Sport) starts from 1st gear, higher shift point and will be less 'eager' to shift to higher gears taking into account vehicle speed and engine speed (RPM).
Manual on our cars gives you manual control, but the shifts are not faster than S. Mainly because in Manual, you need to know the lag in order to time your shifts properly (both up and down). If you upshift with the paddle too late, you will not have a smooth shift, as there is a noticeable lag between pressing the steering pedal and the actual upshift or downshift - therefore you need to know the car and shift earlier than you would on modern cars where manual mode shifts almost instantaneously. On downshifts it's even worst, expect a full second+ before pressing the downshift pedal and the transmission shifting down a gear (in our W204 C63 it rev-matches which is nice especially for those years).

The traction has three settings, ON, ESP Sport, and ESP OFF. When you quick-press the traction control button, it is partially off, and will give you little wheel slip or angle of slide. If you press for 3 seconds, it's fully off and you're on your own.
I have 275s on the rears of my C63, it fits with no spacers (on aftermarket rims 19" instead of 18", similar offset, but I believe 0.5" wider rims than stock). It was important for me that the tires do not stick outside the body or rub, and they are flush and do not rub.