Why are we still talking about Red Rider?
Althouth it is a fun gun and could be accurate anough with cans at short distances, I would advise against shooting steel BBs in a non-controlled setup (without a trap). BBs will ricochet off of almost everything hard while pellets flatten and deform (pellet will ricochet sometimes as well, so caution is key)
You need about 6 ft pounds of energy *at the target* to penetrate fur and skin and still cause enough damage to humanely put down a small animal. Red Rider will produce less than 1fpe *at the muzzle*.
OP, get a Crosman 2240 (co2) or 1377 (multipump) for plinking - loads of fun. I am using a heavily modded one for target practice, it is more accurate than I will ever be
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careful, though, you will be modding it non-stop and will buy another one so you can mod it differently
Crosman 1077 is a nice co2 plinking rifle for summer fun with 12 pellet mags.
For pest control you are pretty much stuck with spring or gas ram powered rifles if you don't want to deal with PCP. A decent scope (with adjustable objective - a must if your distances vary wildely) with mounts will run you about $100 alone.
You may have good luck with a cheaper rifle and a stock scope, but shooting springers take a lot of practice, and anyone claiming consistent succesful kills at 50 yards are either GReat shots or... well, hiding the percentage of misses, let's put it that way
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. Consider this - you will need to be consistently within a quarter size group or better at your intended distance for head or a neck shot - try it out... practice until you can do it