Thats hard to say. A good action job and good barrel fit up will improve the effective range. But alot goes into long range shooting. What barrel length and twist, and especially chamber, will shoot the kind of bullet that you would need to kill at long range. I hear alot about the berger vld bullet these days. They say those things are great out to 1000 yards, but will your barrel and chamber shoot it? Are your reloading methods up to the task? I believe a trued rem700 action, with a quality barrel, a great trigger, good stock bedding, and a good scope, will get you where you want to be. If you can find the rifle at a decent price, work that gun over with small tweeks that are affordable. Spend the money outright on the scope you want. Good investment. Then the stock you want. Get it properly bedded. Get a trigger job. Get as much of the other tweeks as you can afford. The svl barrel deresonator works wonders on factory barrels. Think about a tubb speedlock kit. Then concentrate on shooting alot. Trigger time is most important. Work your way out to where your comfortable.
Here is a project that i did. I bought a left hand rem700 bdl for 400 bucks used. It didnt shoot well. After about 5 years in the safe, i bought a hs precision stock, a leupold vx3 3.5x10 scope, dual dovetail rings, and did a trigger job. I tried several different loads and bullet weights. It shot worse than before. One night on the couch, i was snapping in the trigger and working the bolt. I noticed the barrel was vibrating very badly on the snap, so i bedded the action to the aluminum bedding block, and cut the groups down to an inch. Then i bought an svl barrel deresonator which is basically a rubber donut that slips on to the barrel. It shoots 3/4" groups now with a sierra 150gr sbt and a nosler 150 ballistic tip. I killed a buck with it at 400 yards shooting downhill at 8500' elevation. Shoots nice. But its not a 1000 yd gun. But im not a 1000 yard hunter. With a action job and a custom barrel, and better ammo, the rifle could be a longer range gun, but i like to get as close as i can. The horns end up bigger when i can see and judge them.
Bergers are load sensitive. They have a bullet called a length tolerent bullet, but i know no one who uses it. They arent cheap either. I have used berger vld match bullets at the 1000 yard line in my 308 match rifle, and they were worth the cost. But the load development was alot of work. I went back to sierra matchkings. Much easier. And still very effective at the long line. I think a guy needs to try several different bullets to see what works best. Again, trigger time is needed to shoot long range. I had darrel holland true and rebarrel a rem700 to 25-06. I put a mcmillan general pupose hunting stock on it, and had it bedded by a really good gunsmith friend, and it shoots scarry little ragged one hole groups. Think about this, if you are spending the money it takes for mcmillan stocks, berger bullets, good optics, then the 7-800 dollars for a custom rebarrel and action job really isnt that much more.