I really want to have an Accelerated Start game where you can choose your race instead of being limited to the Terran Alliance. Do any of you guys know a (simple) way I could change the code and make this a reality, or do you have a download of a mod with this available?

I don't believe the scenarios support selectable player race, but if you want you can just make a copy of the Accelerated Start.gc2scenario file with the PlayerRace= option near the top of the file set to the id number for whatever race you want to play.

AFAIK the values for the races are the same as the NameX= number in the second section of the file, minus one. Make sure that if you want to use Thalans or Custom, you set them to 1 in the [ACTIVE] section as they're not on by default in that scenario.