The load data for copper bullets is different. If using Barnes bullets you can get load data from their website.
http://www.barnesbullets.com/information/load-data/
Sometimes the same powders work well enough, but the load data is much different.
The Barnes bullets shoot more accurately when seated deeper in the case than most bullets. You'll need to experiment with seating depth for best accuracy.
They may shoot accurately at extended ranges, but are not a good choice for long range hunting. They need a lot of speed at impact in order to expand. If they hit game at speeds under about 2000 fps they don't expand reliably and a lot of guys prefer speeds closer to 2200 fps. I know Barnes says 1800 fps, but bullets I've seen that hit below 2000 fps did not impress me with expansion. A bullet such as the Bergers, SST's or Nosler Ballistic tip will expand at speeds as slow as 1500 fps or so and are better options for long range hunting.
You need to drop down at least 1, maybe 2 bullet weights for more speed with them for best hunting performance. If you would normally use a 165 gr bullet, then a 150 or 130 is a better choice with the Barnes bullets. A 165 only starts at about 2700-2750 fps and will drop below 2000fps at fairly close range. Look at the loading data. If you can't start it at 3000 fps, keep dropping weight until you can. The 165 and heavier bullets are best used in magnums.
And you don't need the heavier bullets with copper. Traditional lead bullets lose 20-50% of their weight at impact. That means a 165 gr lead bullet @ 2700 fps ends up weighing 80-130 gr after impact. A 130 gr copper bullet @3100 fps will still weigh 128-130 gr after impact and give much better expansion and penetration. This still keeps me above 2000 fps beyond 400 yards.
For what what you want to do I'd look at a 155 or 168 gr Berger. They have a higher BC, shoot flatter and are more accurate. They make a hunting bullet and target bullet. I've found the hunting bullet to be just as accurate. They are designed to stay together for 2-3" of pentration then basically explode in an animls chest cavity, even at quite slow speeds. Not a good choice for taking large game at bad angles because you don't get deep penetration like the copper, but will kill better at all ranges if you put one in the lungs. They are cheaper too, about $45/100 vs about $30/50 for copper bullets.