If I lived in the US I would definately enjoy this type of competition. As far as I am aware there are categories within 3 Gun comps which group by iron sights only...optical sights on rifles only...then open categories which can have optics on anything and speed loaders for the shotgun stages. So letting us know the weapons you will be using might help on determining which division you would likely fit in.
Most rifles are AR platforms as the ranges they are held at are often only able to offer short range stages for the rifles out to 200 yards. .308 scores major and .223 scores minor but central hits count the same. Most seem to go for a .223 but again it depends on what you have.
Shotguns are nearly always semi-auto as the gas cycle systems are quicker to return to target than pumps due to less recoil. Slug barrels or interchangeable chokes to enable a slug to be fired are again the norm.
Pistols are 9mm and above and can be anything from stock factory to custom race guns.
If I were doing this I would use my Benelli M90 multi choke combat shotgun which groups slugs best using a half choke fitted and has an illuminated TV screen red dot sight....I would try and get my custom Para Ordinace P14 .45 fitted with a Gold Cup barrel and trigger back from abroad...and rifle wise I would go for a Custom AR platform chambered for the 6.5 x 47 which is the best calibre choice for this type of comp IMO and can work by altering the lips on .308 mags and may work by altering .223 mags but I have never gone down that route myself...prefering the larger mags so I can seat the bullets out slightly more.
Knob Creek does a good 3 Gun Comp I believe which is near you...so you could combine this and checking out the Busse stand <img src="/ubbthreads/images/graemlins/thumbup.gif" alt="" />