All depends on what you are interested in and the type of shooting you will do. Here are a few suggestions:
1-Highpower Ar style rifles in .223
2-Benchrest Bolt gun in many different calibers, I prefer the Rem 700
3-Sniper Matches .308 Remy
4-600 prone .308 or .223 both work, I like the .308 due to the wind factor but have seen many times the .223 shooter winning.
5-600-1000 prone .308, no smaller, again the 700 Remy gets the nod.
6-3 Gun Competition AR in .223 or the Mini in either .223 or 7.62x39
Either the 700 Remington or the many variants of the Savage 110 will work in bolt guns. The Savage is less expensive and most likely more accurate out of the box. They are also easy to build your own, the web has lots of plans on DIY Savage target rifles. Good luck!
223 and 308 only denote the bullet diameter, not the cartridge they are being used in or the rifle they are being fired from.
Now, BAT, Noseka, and several others make good target receivers. Lilja, Shilen, McGowen, Kreeger and several others make good target barrels. McMillen and Lone Wolf make good target stocks. Nightforce, Leupold and a few others make good optics. Norma and Lapua make good brass. Berger, Lost River, Nosler, Sierra and a couple others make good bullets. BUT, without a great gunsmith to assemble the package with care, not even the best collection of parts will proform at it's potental.
On the flip side, you could start with a Rem rifle, have the receiver trued and bluprinted (after which the origional barrel won't fit anymore), replace the barrel and stock and you'll still end up spending about the same amount of money as if you'd started with a high end, but ready to build, receiver.
Of course if all your wanting to do is play at poking holes in paper, than a Salvage or Dumchester bolt gun would work just fine
I have the Remington 700 varmint SPS 26"bbl. in both .223 and .308. I have no complaints with accuracy in either and love em. Remingtons have alot of after market parts available. I would also consider the Savage models that are known for accuracy, lower price and ease of rebarreling.
I have to admit, I am a savage fan. Personally, I started with a Stevens 200. You know, the cheap savage. After a little custom work, she is a .223AI shooting 3/8" consistantly at 200 yards. If you do not believe me, you are more than welcome to meet me at the club and try her out.
There is nothing wrong with a Rem 700, or a Ruger for that matter. The only strike against the Ruger is that some one long ago said they thought that push feed rifles had an edge over controlled round feed guns. I am sure Tailgunner will insist on telling you about his -06AI I give the edge to the Savage for ease of, and frugal manner in which barrels can be changed.
Now, you have to decide on caliber..... How far do you want to shoot your targets? 200yards or less the 6mmBR is king, err, tied with the .30BR. 300 yards is pushing it with either, and 600 is pretty much out. Not that they cannot get there, but other chamberings are much better suited. .308Win is good for 600 yards, but .260 Rem is much better. Both will do well at 200, but not as well as 6mmBr, or .30BR...........................I could go on all day. How about a little more specifics on your end, so we can make better asanine suggestions on our end