A few pages back will be my post on the Stevens 223 I worked on. It did average 1/2 min at 200yds. Did some nice 3/8" groups at 100yds too.
I bedded the action and barrel nut, free floated the rest. Tuned the trigger but eventually that went out for an SSS unit - hate heavy triggers.
The factory Stevens barrels can be great shooters but almost all will open up when they get hot. I have yet to find a Savage or Stevens that wouldn't hold MOA or better giving a good load work up.
Many shooters are reporting 1/2 MOA type accuracy so mine is not an oddity.
Rems shoot. So do Tikkas and Winchesters. However, with any factory rifle, you can get some duds for barrels.
For what you are doing, I would suggest the Savage 12FV or another version with a stock to your liking. That way you get a heavier rifle right away with a decent trigger. The heavy barrel will be more tolerant of more shots before overheating.
I usually just open up the forend with LOTS of space around the barrel. Seems to work. Or you can reinforce as described or use plywood on the outside. Seal and spray paint and they look just like composite stocks. Makes for a great dirt cheap project.
From there, you need to do some load work up. I have shot 75gr Amax exclusively in mine. Benchmark and Varget (prefered) lit with CCI BR4 or 450 (prefered) in Win cases will get the job done. I use Lee collet neck dies, Redding body die and an RCBS seater. This can make ammo with under 3 thou runout at the bullet. More then consistent enough to shoot as good as the barrel will allow.
Odds are the throat will be too long for an OAL to fit in the mag. No matter as single feeding is not a big chore.
Get some Burris rings w/inserts and a decent scope. That will do more to improve your shooting then another brand of factory rifle.
As for hitting a pop can at 500yds, that will just take some practise and consistent ammo. The better BC of the 75gr Amax helps alot the further you want to go.
There are three articles in my sig line that will help you get started in LR shooting. Using my rifles, I have had every newbie I have taken out hit clay pigeon sized rocks at 500+ yds within a dozen shots.
If you can hit a small target at short range, LR just means you got to lean into the wind a bit more.
I enjoy using a scope with a mildot or hash mark reticle because it helps so much with wind doping.
Final thing, when working up a load, watch for vertical stringing. If you can dial it out, awesome. AT least try and minimize it cause it will drive you insane the further you try and go.
How far can a 75gr Amax out of a 223 go? Well, I think I have pretty much covered that. 1 mile is well within possibilities
AND a Savage will make the trip.
Jerry