Lee, if you are still 'learning' at the 300-400 distance, I strongly suggest a cartridge that will be cheap to buy (or load), easy on the shoulder, allows long barrel life for your learning curve time, is very accurate, has easily-bought match ammo/bullets, and is effective out to twice your current 'learning' distance. As Jack Roberts has said before, you can easily burn out a barrel learning the art and science of long range shooting. The .308-based rounds fill this bill nicely, starting with the .308 itself. Not sure if anyone makes match-bullet loaded ammo in 7-08 or .260, but you sure can load the match bullet components yourself. This case size will wheeze a bit out towards 900-1000 yards compared to the bigger ones, but will give you way better barrel life, cheaper brass and powder costs, and less shoulder aches. Plus you will become a very good wind-reader. ;-)
I don't know how big a critter you are planning to hunt or how far away you want to shoot it, but the bigger and further you get the bigger your round should be. A big magnum thumper will perform better but cost more, hurt more, and eat your barrel faster. A good compromise might be a .30-06 based case (.280 handloaded gets my vote) or a 7mm/.300 short magnum, if you need that much. The old 6.5 Remington Mag (short-action) is another thought.