What is the best pellets (177-4.5mm) for hunting

+1 to what intenseaty22 said. You have enough fpe (foot pounds of energy) for small game with your airgun. Use heavier pellets. They will carry more energy into your quarry and will more likely be the most accurate - but only trying different pellets will give you a definitive answer. I start with JSB brand and go from there. Most essential thing will be shot placement.
 
My Crosman break barrel NP1 loves RWS super points 8.4-5 gr In my experience the 1000fps like a mid range weight 7.9-8.5gr but have had luck with 10 +/- gr, but limits the range Like every one else says, each gun is going to like some thing different.....I like Domed,Points, and Hallow Points Seem to get the best accuracy with Super Points, but the others listed are pretty close in accuracy.
 
My best luck has been with anything your gun will shoot well in the 10gr range. I have harvested many woodchucks and skunk sized game with one shot with that weight range going 920fps. Shot placement is key with .177. Body shots will take time to kill but brain is always lights out. I always went for the ear canal whenever possible with instant success out to 60 yards.