I'm not an expert, but I will help you as much as I can.
The first thing is to practice shooting at range!
What model? seven, 710, 700, 7400?
Remington uses a 1 in 9 1/8 twist (you should check this out by marking a cleaning rod and measureing how many inches it takes for the rod to make one full revolution). The reason I say this is because, generally speaking, you want to have the heaviest bullet that you can stableize for your longest shots - less wind resistence and more power. In order to stableize bullets over 100 grains in a 243 you should have a 9 twist or an 8 twist. Pobably getting too technical and your gun should will work very well with the 75 - 95 grain bullets at range. Make sure the barrel is free floated ( you can do this yourself) and if possible have the chamber bedded (@$80). Have the trigger set as low as you feel comfortable with (700 only)(@ $40). Use the best glass you can afford and practice.