My group and I all decided to learn the 4th edition and get the game down... To the point where we do not need to be prompted on what to roll or having to look everything up.

Rather than go through boring drills. I was wondering if there was a preconstructed run that was great for beginners learning the game for the first time.

Try This Thread

Checking that thread out, thanks in advance...

Food fight! The classics are great.

SR4 Missions Free Downloads
Free Quickstart Rules (Food fight)

This! Use the stats from the Food Fight 4e version, but ditch the stupid plot. Gangers tearing up a Stuffer Shack is far more fun than a shitty botched assassination. Plus it's traditional for me to start off every campaign with Food Fight, and I carry over plot from each campaign if I have players sticking around (a run the last group they were in did may pop up in the new game as an Easter Egg), it's far easier to explain how a gang will hit a Stuffer Shack over and over, but much harder to explain an assassination getting completely botched over and over again.