Your basic consideration when arming someone.
There is a huge difference between predator shooting and predator hunting. In the latter you are set up, have some sort of a gun rest and are, probably, calling them within range. There is lots of time to focus on the target and squeeze off a shot, probably at a long, predetermined range at a fairly stationary target. When there is a predator attack: it is an emergency which consists of grabbing the nearest gun, running out, adrenalin pumping, and trying to get off a shot before a moving animal disappears with one of your chickens. Under these conditions you need something you can throw up and shoot as quickly as possible, at short range, without taking a lot of time to aim. In this case a scatter gun would probably be the best although there is a chance of collateral damage--you'd probably take out the chicken as well--and the injury might not be immediately fatal. A small bore rifle will work as well if the shooter has had enough practice to be reasonably accurate and aim it quickly which makes something that uses fairly cheap ammo to facilitate practice a good idea. (Keep in mind one of the things that makes the biathlon so tough is not the cross-country skiing or the shooting, it is the slowing down of the skier's heart rate to allow him/her to shoot accurately--if a trained athlete has a problem with this imagine what your average BYCer is going to go through.) Either way I would be more concerned about stopping the predator than killing it immediately--at close range it would not suffer very long before it would be dispatched. (Probably less time than it would take to reach an animal after a 200 yd. nonkilling shot.) That being the case a .410 or .20 gauge shotgun with #4 shot would be the best choice for a small person or a rim fire rifle with open sights. Anything bigger, i.e. .12 gauge or larger bore rifle, would probably kick a little to much and/or take expensive ammo both limiting the amount of time one would spend learning to use it. A handgun might work as well but they are notoriously inaccurate for most people and their ownership is more tightly regulated.
Couple of other thoughts:
I too would prefer to live-trap any predator. The problem with this is either you have to keep the traps going 24/7/365 which means constant monitoring or you have to lose a few birds before you set the thing up. In my case, most of the predator losses have been sudden, one shot things where the animal shows up, kills a few birds and then either disappears or is eliminated. While we have a lot of candidates for the role of predator living in this area, few seem to need to fill the position unless driven to it. I prefer live and let live until the animal becomes a problem then eliminate that individual by either trapping or shooting.
Also, I read some of these posts with my hip boots on in re to shooting prowess. 200 to, especially, 500-yd shots are sniper distances and, while I don't doubt they can be made, they do take a lot of practice and very calm nerves to pull off. As a teenager--many years ago--I was a good marksman at 100 yds with open sights and had a bunch of trophies to prove it but I was putting a lot of lead through the barrel to get there. I don't think it is something an average Joe or Jane is going to pick up by shooting up a box of cartridges over a weekend or two.
