Greetings,
I have used a RWS mod. 34 with a Beeman scope for several years and have taken may Tree rats and rabbits with Beeman Silverjet .177 pellets. These pellets have proven to be worth the extra cost due to the increased seal within the barrel. I have taken rabbits from as far as 25 yrds. Lucky shot I guess! Just a thought for ya, Look into the Crossman Quest 1000 before purchasing the Winchester. I compared both, side by side and the Crossman felt much smoother and refined for about the same cost. I also own a Beeman that fires approx. 700 fps. and have taken several small game with it at over 50ft. This Beeman is in the same price range as the Winchester and Crossman and is far better quality, just slower! If you have the extra $, look into the Gamo NRA special edition and support the NRA, It's an awsome gun!!!
Good Luck and be safe, you could put your eye out ya know! HA HA