Imo he brought the Saiga for breeching the glass but decided to use the AR for that at last second. The fact he brought 300+ rounds for his AR and only 20 for the shotgun supports my theory. He might've also wanted to use it for breeching doors or something similar.
As for the Glock 20 in 10mm, Adam was extremely nervous about not being able to kill himself or surviving his suicide, so he picked a pistol a bit more powerful than 9mm for a quick and painless death. He knew that Dylan suffered for a bit after shooting himself with his 9mm.
As for the 9mm, I think he brought it as a backup to a backup. He was very nervous about possibly being taken down and surviving so brought it in case his AR and 10mm jam if he gets tackled.
I think he chose the AR-15 because it's a reliable, accurate, easy to learn, relatively powerful weapon with manageable recoil, easily found ammunition, and cheap magazines.