You've got quite the budget but the truth is any AR that shoots without jamming will work for 3 gun. I would recommend sticking to 223/5.56 unless you have already confirmed with the clubs you plan on shooting with that they do recognize major PF (or even allow it for that matter), you don't mind competing against fewer shooters, are going to shoot a major PF handgun AND can afford it without skimping on practice. Most people are still better off with a minor PF rifle anyway but shoot what makes you happy.
What is going to be more important than the model of the gun itself is finding out what distances the matches will be shot at so you can pick the best optics setup. 1x red dots and 1-4x scopes are quite popular for shorter ranges. Optics seem to take more abuse than rifles do when you're on the clock FYI.
New gun, same ol' shot.