Hi David;
Welcome to the long-range game. Are you planning on shooting fullbore/long range competition? At what distances are you planning to shoot?
So it's a 223 - my first long-range gun was a 223 Savage Model 12 - a good shooter. It has since been converted to a 308 with a custom barrel and trigger.
What is the rate of twist in your barrel? A 1:7 rate of twist is ideal for the larger bullets (80 or 90 gn) which will allow longer ranges up to 1000 yds.
Some basic things that will increase accuracy include bedding the action, making sure the barrel is free floating, reducing the trigger pull and reducing the spring force on the ejector.
If you are using a tripod off a bench, then a 3" stock fore-end or 3" conversion plate is useful. If you're using a bipod make sure it is a good one that is stable and recoils straight back. A Harris won't cut it. There is an M-Pod for sale on Gunnutz now that would be super for prone shooting.
The rest, like in BR shooting, is all about good shooting technique, good components, good case preparation practices, good reloading equipment and some time spent in load development. I assume you do reload - in any case you'll go broke and will be disappointed in factory ammo.
Hope this helps.
Good luck and have fun - it IS about having fun!!