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You'll have to talk to the local La. racers to get a sense whats involved local to you. There are a few racing organizations but I dont know which serve your area. WERA is one that I know might. NESBA might be one too. Your local track should also have info on that, possibly.

If I wanted to get into racing I know the local track here holds a racers school which is required before you do your first race. Completing it gets you your racing license. Its only a weekend thing.

Across the board, your bike's got to be race prepped too-not just trackday prepped. Its MUCH more involved.

check the home page of gstwin- http://gstwin.com/ there's a racers corner there and that has a bunch of info that you might find useful.

you know what would be fun? some sort of race where only 500cc twins are allowed 

they have them...oh wait, they also allow sv's in there too. D'oh. Locally, willow springs started a BOTT race series racing 500cc twins.

WERA rules:

QuoteLIGHTWEIGHT TWINS SUPERBIKE EXPERT & NOVICE and LIGHTWEIGHT TWINS SUPERSTOCK EXPERT & NOVICE
Up to 800cc air-cooled twins
Up to 750cc water-cooled twins with 3 valves
Up to 700cc water-cooled twins with more than 3 valves
Unlimited singles based on Formula rules (Superbike only)
-No 125cc GP machines,
*Buell Firebolt and Lightning, BMW Boxer Cup machines, Ducati 1000SS and 900SS, are allowed under Superstock rules (with slicks) in LWTSB only.
*There are no bodywork limits in LWT.

LWT and the "D" class are all dominated by SVs, built EXs, and other stuff. A (any!) GS is a rolling chicane. Same really goes for even Clubman too and for CCS's light twins class, which used to be the only classes that the GS had more than a snowballs chance.  The GS really isn't compeditive in anything these days.  Its a great track bike, which is why it has persisted on the race track for as long as it has, but it can't compete with bigger, "better" bikes.

Getting into racing is very easy. All it takes is a surplus of time and money 
My advice is to first do some track days to see if you are really interested in the commitment racing requires and then figure out which clubs hold races at tracks convienent to you. Go to a couple of events and volenteer to cornerwork. All you have to do is show up a bit early at the gate and sign up.  You will learn alot about how race events work (schedules, flags, racelines, etc), you will also see how well each club is run and get to know the people that run it and make it all possible.  They will even buy you lunch and give you gas money.
After that, sign up for a race school to get your license and away you go.