Hey welcome to TFL . Let me start by saying your 223 choice will work but I recommend a 308 . Howa makes a 20" heavy barrel combo rifle & scope in 223 and 308 for around $600 out the door . What ever rifle you get it should be a heavy/bull barrel . The reason I say 308 is . It will get you to 800+yds and the ammo is not that much more . When you start shooting for accuracy and long distances your not shooting the cheep stuff . You will want to shoot match ammo and it's all expensive .
Although my balistic calculator says you can shoot a 223 - 1,000yds . It's realy not the bullet for that range . I would say 600yds would be more like the range you would want to shoot the 223 .
This is a video series on long range shooting that is incredibly informative . http://www.youtube.com/watch?v=pwG-D...gJqhUrQRdMSSAf
Before you buy anything watch the first 3 or 4 videos . They are 20 to 40 min long so put some time aside it will be well worth it .