My first "precision rifle" was a 700 ADL in .222. I went custom by purchasing a 24" Gaillard barrel and installed a fixed 12X Leupold. Once this barrel was installed and the action trued and bedded I could scarcely believe what I could do with this rifle. On a still day shooting at a hanging 5/16" chain at 100 yards, I could cut the links and call which side of the link I would cut first. With match bullets and tweaked brass it was a true quarter minute rifle. It was totally unimpressed by changes in loads and shot virtually everything well, the exception being Winchester 55 gr FMJ bulk bullets, but nothing shoots those things well.
Later I blew a wad of cash on a full custom .308, McMillan stock, Jewell trigger, Krieger barrel, S&B scope, and on and on, anyway this thing shoots and it should, but not so much better than the little ADL, considering the difference in cost. The .308 weighs about 20 pounds and the .222 weighed about 10.
For what you need the .223 is a better choice. There is more loading data around for the .223, particularly data for heavy bullets that you will want for long range shooting. I would hunt around for well used M-700 hunting rifle that you can buy cheap, salvage the action and stock, and build your target gun from that. Your budget is tight, but I think its doable. Sometimes a gunsmith will have a barrel lying around that a customer ordered and couldn't pay for and is willing to deal on. You can find good used scopes at reasonable prices in the EE. Fixed power scopes are cheaper than variables, and a fixed 10X or 12X will do you fine. Too much magnification though is a pain on days with thick mirage. Don't cheap out on the mounts, you don't need to spend $500 on them, they don't need to be detachable, but they must be rock solid.
This will get you in the game, and as you can afford it, because you have a sound basis to build from, you can improve the rifle over time. You will probably be loading heavy bullets on the long side, so a single shot adapter might be useful, I liked it in my target rifles that I don't load from the magazine. I remove the plunger from my target gun bolt faces to ensure the round is sitting square in the chamber, but you might find this is more of a pain than a help. It does slow ejecting, particularly a round you haven't fired. If you are handy your can bed the action yourself, but if you end up with a wood stock or a cheap plastic stock, pillar bedding is a better choice and a gunsmith can perform this easier than the home handyman unless you have a well equipped shop. Once you get your donor rifle, get a quote from a gunsmith for a package deal to find out where you are at. The package might include: supplying, chambering, and installing a match grade barrel, truing the action to produce equal bearing on each locking lug, pillar and glass bedding, opening the barrel channel for the heavier barrel, and adjusting the trigger to get rid of any creep or over travel, and lapping the rings. If you have a bullet in mind, you can make up a dummy round for your smith and have the chamber cut to match that length. Just remember that you maximum bullet weight is limited to the rate of twist of your new barrel.
shop around the shops that have new stock will likely be more expensive
