Welcome...very nice choice (why would I say that ?
), congratulations ! 
A few remarks though: The LSD is a must on this car, retrofit is quite expensive (close to 3500 EUR last time I checked).
The performance package is also pretty helpful since it not only includes more power but also a sportier chassis on 2008 cars as far as I remember. Not sure if the performance package was available at that time though. 
I don't know how much you paid for the car but when I looked for a C63 Coupe, I was also checking on used C63 sedans and I found one with less than 20k km, incl. performance package and driver's package, a 2012 car, for less than 60k EUR. I also found a C63 sedan with performance package, 2010 I think, less than 20k km for 49k EUR. Both cars sold through official Mercedes dealers, incl. used car warranty.
The C63 facelift also includes the MCT gearbox and the SLS-derived gearbox control unit (C, S, S+, M and RS), also some major interior improvements and of course chassis improvements.
Don't get me wrong, this is a great car but especially the lack of LSD will be a huge issue for you sooner or later. I had an E55 AMG without LSD and I drove only 2000 km before I retrofitted the LSD. Quite an expensive experience, I paid at that time almost 7k EUR for a LSD, a Vmax raise, a new steering wheel and a different automatic tranny software. The car also had to stay over a week at AMG in Affalterbach and I had to drive there twice forth and back, time is money, right ?!
A couple of tips for you I got from AMG pros while looking for the C63 Coupe I got:
1. Always warm up the engine as good as possible, the V8 6.2 l engine is very sensitive to cold temperatures
2. Removing/exchanging the center exhaust silencer, many do that to improve sound in a cheap manner, reduces engine power by around 30 horses, no kidding
3. If you want to improve the sound, the Superspring exhaust system with new 200 cell cats is the way to go, no power loss, even a slight power increase of up to 10 horses (with software adaptation up to 30 horses)
4. LSD needs a mandatory oil change at 3000 km, engine oil change should be done too at this point
5. Software only ECU upgrades (Brabus, etc.) work pretty well but power increase is usually in the 30 horses range, with sport exhaust and 200 cell cats, in the 40s, not the sometimes promised 50-60 horses
6. Repairs on the C63 can be "pricey", get a used car warranty if you buy it used (Mercedes dealers preferred)
7. The C63 is very sensitive to tire choices, especially regarding traction and sidegrip on the rear axle. Stick with the Mercedes AMG recommended tire sizes and types (Mercedes AMG uses "M" ratings, similar to the Porsche "N" rating), wider tires on the rear (summer and winter) are a disadvantage. Maximum tire size for rear axle is 255s (possible up to 265s but not recommended), for winter tires 225s. Caution: The LSD can be damaged with wrong tire/rim choices. Best choices (from experience) so far: Summer tires Conti 5 P and Winter tires Conti TS810S, both available in M0 configuration. Avoid Yokohamas, which are often used for the C63.
Have fun with your car and get that LSD retrofitted as soon as possible. You won't regret it.
Unless you want new rear tires every couple of months... 
Check out this .pdf file for the options you can retrofit on your car.
C63.pdf
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RC (Germany) - Rennteam Editor Porsche Panamera Turbo S (June 2012 delivery), Porsche 997 Carrera GTS Cabriolet PDK, BMW X5M, Mercedes C63 AMG Coupe PP/DP, Mini Cooper S Countryman All4