TinyTim offered good advice. I don't know about the other brands mentioned, but generally, the Barnes Bullets ( the "only" bullet we've used since the early '90's) are happiest with a lot of "jump". Assuming that your rifle will shoot other bullets with acceptable accuracy..... you should have good success with the Barnes Bullets! We are not shooting high dollar, specialized long range equipment, (these are relatively lightweight [for caliber] "hunting" rifles") and yet can get sub-2", three shot groups @ 300 yards....with pretty good regularity!
I don't think that it is as important as with the original Barnes X Bullets......but, I suggest when shooting the Barnes Bullets, you thoroughly clean all traces of "gilded " metal remnants from your bore. Many years ago, it was suggested that when shooting the original Barnes X Bullets, treat them as though they were cast bullets. Use them in a bore cleaned of "any" copper / gilded metal fouling! We've always had good success with the Barnes Mono bullets.....even when other folks were terribly dissatisfied with their accuracy! The original Barnes Mono bullets were good, the new Barnes Bullets...... exponentially better! memtb