Be careful Sniffer, 3 Guns really addictive
Your pistol and shotgun are fine for 3 Gun. IMHO 16" or 18" rifle barrel is the safe bet for most matches. If you go with SBR you will have a tough time with the 100 metre + targets, some of which can be 4" clays or small water bottles etc. Almost all the Boyz and girls will run an AR 15 in .223 of 5.56. And in some of the US matches the rifle distances can be 200, 300, 400 + metres out. In canada most I've seen thus far is 100 metres, though at my last IPSC rifle match the MD was talking about 300 metre COF for his next match. SBR rifles with a good operator can kick ass On the shorter rifle stages, but will struggle at distance. Also heard you will likely have probs trying to bring anything less than 16"s in the States.
As another poster suggested, best bet is to find a local match and contact the MD and ask them the questions. Each MD and range are going to have their own 3 Gun rules. Most are pretty standard but some can be range specific. Most will also take any decent holster course you have successfully completed, including club level courses. Again, different ranges and matches have different rules. In the States though some matches don't require any holster course. I personally would not recommend you doing a 3 Gun match without taking some type of holster course. It's a fast dynamic sport and once the adraline starts pumping the chance of a potentially serious mishap is amplified big time...especially with newbies.
Almost all the guys/gals you meet at a 3 Gun match will be willing to give you advice and support. We were all there at some point. So try not to overthink it to much just get out and shoot one. And when you do, take it slow and deliberate and make your shots! Accuracy is very important in 3 Gun and will often trump some speedster who blisters through the COF and has a bunch of Mikes and or + time shots.