Been having a problem with "cold" or first time start-ups with my '05 R53, stumble (revs unable to get above 1,000 RPM until about 5 seconds and feels like it's going to die) on first start or if the car has been sitting for more than 4-6 hours after shutdown. Battery voltage on startup dips to ~10.5 volts, and is currently sitting at ~12.2-12.3 volts. Checked the ignition coil pack and discovered some black gunk on the terminals and I wiped some of it off with a rag, then proceeded to start the car and it didn't have as much trouble. Should I replace the coil pack and wires?

Photos below:

 

Those don't look too bad.
Try sandpapering all four & the matching plug wires - add a touch of di-electric grease.
(For some obscure reason, corrosion on the #3 terminal is very common).
That may be all it needs.