I dont care the round, a Light bullet at 250 yrds with a little bit of wind will drift quite a bit and loose a lot of punch. I have found that at those distances, we are way better off with a .243, 6mm, and up. Look at what a 30-30 does at 250 yrds. Look at what a 45-70 does at 250 yrds. All of them are capable to reach that distance, but drop on slower rounds is getting really big, and drift on light rounds is getting really big too. I suggest a round that is zipping so its flat, and has some mass so the drift is not too great. BUT all that being said, the 17 WSM is the only rimfire that I think could do something good at that distance. IF YOU are a good guesser on the winds or if its calm. Just saying.
Dyslexics of the world - UNTIE!!