I've been thinking about this and many people made mention of it  - we should add something in here about the family of cartridges known as the .22RF's (rimfires).
While not the end all by any means, they are cheap and easy to both tame and control, especially for new shooters. The low cost should not be underestimated when we're talking about farm use, either. Last time I looked, a box of fifty Federal Champions could be had at 
WalMart for $1. I like to shoot and reload, but that is not for everyone - the .22RF's will give a lot of shooting for little money without resorting to such efforts. 
There are two classes of RF's; the Long Rifle (LR) and it's kin, the short and CB and the Magnums or WMR's (Winchester Magnum Rimfire). 
For vermin and the smallest of game the LR's are de riguer and have been so for a very long time. In my day, no boy was complete without a .22 rifle. These guns are available in single shot, bolt action repeaters and auto-loading models and they are low cost, to boot. The Marlin Model 60 is one of my favorites, for example, and holds 15-20 rounds of .22LR and can still be had for 75-100$ used. As accurate as you'll ever need, it will last forever and take care of many a pest in the process. With the right ammo, rabbit and squirrel are on the menu anytime.
For close in vermin like rats, Starlings and so on, the shorts and CB's are perfect. Really just reduced power versions of the .22 LR RF, they offer another wrinkle to the shooting of these little guns and are best out to about 30 yds. They make about as much noise as a capgun and so wont disturb the neighbors - and no rat in town can withstand them. Their main drawback is that they wont cycle a guns action, so have to be manually loaded and extracted. This is the bolt action rifle's territory.
The .22 WMR Magnums are a serious step up in power over the other .22RF's. With the right ammo, they can handle larger game like racoons and smallish dogs, such as coyotes and foxes. This is taxing their ballistics a bit, but in a cool hand this is more than possible. The downside is that the guns for them cost more to buy and they cost more per shot than the .22LR's.
But anyway you look at it, no battery should be without at least one .22RF.
Many have made mention also of the gunbearing rights we as Americans enjoy. Whether you hunt or not, own a gun for protection or shooting enjoyment or choose not to own one at all, the privilege to do so should not be one you lightly sell away in the name of security or "safety" entrusted to a government or police force.
The founders of this nation felt it was everymans duty to be both a soldier and a citizen, and made provision for you to arm yourself as you see fit. It is only in a nation where that right is abriged or forfeited that the leaders can do as they please to their subjects. Our forefathers knew that, too.
Do not be willing to vote away your right to own a personal firearm, when that agenda is sold as a deterrrent to crime or as a way to preserve the peace. Neither will be ultimately satisifed by the effort and you will live a life of servility for doing so. Here's a tidbit for you ....
+ Guatemala established gun control in 1964. From 1964 to 
1981, 100,000  MAYAN INDIANS, unable to defend themselves, were rounded up and exterminated. 
  
Mayan indians? You've got to be kidding...
                   
+ Uganda established gun control in 1970. From 1971 to 1979, 300,000 CHRISTIANS, unable to defend themselves, were rounded up and exterminated.
+ Cambodia established gun control in 1956. From 1975 to 1977, one million 'EDUCATED PEOPLE', unable to defend themselves, were rounded up and exterminated. 
In the 20th Century, the TOTAL number of defenseless, unarmed people rounded up and exterminated where gun ownership had been taken away is something like 56 MILLION.   
We all know that our country is not perfect and has problems, but Im sure you get the point.
Okay, so much for soapboxing. We now return you to your regularly programmed topic.....