Since you have shot some steel matches, you already know that there are no two stages alike. (or it should be that way) 3-gun matches are the same way. No two alike. Sometimes, on one stage, you will only shoot the rifle, long distance. Then other stages you may start with the rifle, shoot some targets close up, (I have shot targets so close the muzzle blast blew the target off the stand. LOL) then transition to the handgun. Once in a while you may start with the handgun (the other two will already be loaded and placed somewhere on the stage) after the handgun part, you will transition to one of the others for a while, then the remaining firearm, only to finish with the handgun. Most of the time the stages are set up to shoot at least 2 firearms. (except long range rifle)
The firearms you mention should do the job. Any handgun 9mm or bigger. Rifles are usually restricted to ANY military caliber. Most people use an AR of some kind. Shotguns are usually 12 ga. The number of people using pump vs. semi-auto is split, most people use a semi-auto, but I have seen a pump win the stage.
Why do you need to change the barrel?
I did get a new barrel on my 1187. It has a 20” now. I changed it so I would have rifle sights and be able to shoot slugs. Make sure that your shotgun is able to shoot slugs. With some chokes, it is not a good idea to shoot slugs through them.
One of the most time consuming things in a 3-gun match is re-loading your shotgun. Practicing this is recommended. If you reload your rifle on the move (best time to reload all weapons, is between shooting positions) then you want to check to see if you can put a FULLY loaded mag in, when there is a round in the chamber, and the bolt is closed. With some firearms, you will not be able to do this. (H&K, Steyr, etc) I am not sure about an AR. If this is a problem, the answer is to load only 18-19 rounds in a 20 round mag. You do not want to find this out in the middle of a stage.
Sorry I do not know about matches is AZ. If there is a IPSC chapter in your area, they may be able to steer you in the right direction. Check with the guys running the steel match, they may know of one. Hope you find one. 3-gun matches rate right up there with sex and/or a winding mountain road in the summer on my scooter, in my opinion. Above all, be safe and have FUN.
The gene pool needs chlorine