.177 cals would work, but you would need to be at a pretty close distance, and have a perfect understanding of the power of your gun. .22 is a whole lot better. Heavier, flatter trajectory, less likely to be pulled of course by the wind.
If you are on a tight budget, by all means go with a .177, but get the strongest one in your price range (fps wise, but don't get a freakin gamo. They are all garbage every single one of them) get something thats rated about 900-1000 fps. That is always with pba pellets, which you will never catch a person who has experience using.
For only about 100 upwards to a few thousand dollars, you can pick up a very good .22 cal with a nitro piston like the benjamin titan (my squirrel and rabbit hunting airgun) or it's big brother, the trail np. Both deliver between 13-15 foot pounds of energy, which is ideal for squirrel and rabbit hunting out to 40 or so yards (granted you have a good scope like a leapers 4-16x40 which costs about $100) (the titan is $150, and the trail is around $200, but trust me it will be worth the money. The scope that came with my titan worked till I got my leapers for christmas) also the hatsan 95 (im not sure of the exact model, but I think they have a nitro piston version as well.
Go with the .22 or even .25 cal version, but with .25 cal, you will need to buy ammo online) whichever gun you choose (all of the guns I listed are under or at $300) you will more than likely need a different scope (the scope on the trail works pretty well, but an upgrade is always fun) you can use any scope you want, as long as the ring bases match the scope rail (dovetail or weaver) and the ring diameter matches the scope tube diameter (1 inch or 30mm. 30mm is more expansive) I suggest any scope and ring combo from leapers/utg as long as the scope has a mil dot reticle, and an adjustable objective lens (AO) my leapers 3-9x40 AO MD IR with utg xtra strength (i think thats what there called, I forgot its been 8 months since I got them) works amazing on my titan. The zoom works good for those down range rabbit shots or up a tree squirrels, and the AO makes it focus precisely (the main reason I bought it was because I could barely see rabbits at 20 yards with the factory scope because it was so fuzzy) im amazed I hit those things in the head.
Just don't use a real rifle scope, because air guns produce sooooooo much recoil inside the mechanism when fired, they will (i have seen it happen before) destroy any real rifle scope within 5 shots. Make sure the scope you buy is rated specifically for air guns and is shockproof (leapers scopes are shockproof) nitro piston or spring piston? Both are good platforms, but with the nitro piston you can leave it coked for hours, as with a spring piston, you can only have it coked for 5 minutes without damaging the spring.
Also with the nitro piston, it is quieter, you don't get that pink or twang sound. Just a soft crack as the pellet breaks the sound barrier or comes close to it. The titan, trail, and hatsan 95 all have a nitro piston powerplant.
Oh and the nitro piston works through all weather snow rain hail sun, hell I went hunting the day after the ditch behind my house flooded, and had water on the trail I hunted on. Just had to watch for snakes. The spring powerplant will seize up in cold temperatures or in wet conditions (trust me its so freakin humid down here) lastly, I live in south louisiana, I only saw snow once like 8 years ago, but I do know with rain, you are going to want something with a fully shrouded barrel, which means the barrel is wrapped in plastic, and has baffling to dampen the noise.
Without this, you will be like me and get a coating of rust on your barrel if you get stuck in the rain. Composite stocks are lighter, but I like the look of a wood stock, but don't get caught too long in the rain.
That depends on how much you're looking to spend. Air rifles generally function okay in rain or snow. But, you do need to wipe them down and oil them after being out in weather.
Daisy 880($45) Crosman 2100($55) Walmant Gamo Hornet($99) Benjamin 392($139) http://www.academy.com Hatsan 1000S($110) Hatsan 95($149) Gamo Rocket IGT/SAT($189) Hatsan 125TH($199) RWS 34($279) RWS 350 Magnum($439) http://www.pyramydair.com.
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