If you are going to range shoot only, the 308 is the way to go. The 223 won't cut it to 1k compared to the 308. This is only my opinion but its correct.
0.25 to 0.50 MOA is gonna be a pot shot with and out of the box factory rifle. Not to say that it can't happen.
If that factory out of the box is your only option, before its ever fired, do the bedding thing, pillar and skim. Threads on here to show how those things are done. Not hard to do well, the first time by someone with your experience.
Do some trigger work if necessary.
Your thinking on glass is proper.
Next step would be to break in the barrel. Go to Lilja's web site for a way to do that.
While doing the break in shoot for groups to get an "idea" of how it shoots. If it breaks in quickly that will be good. If not, run a full dose of Tubbs Final Finish through it. and see how she shoots. Usually there will be an improvement.
Except for the Tubbs process I am assuming factory loads. If the barrel excessively copper fouls after say 20 shots I'd do the Tubbs thing.
With factory loads you are going to get what you are going to get.
As stated in the above post a press and dies is almost a must to attempt to attain your accuracy goal. It isn't that much in $ when compared to factory ammo costs.
By reloading, your bullet, power and primer selection will be greatly increased allowing you to "find" the combination of components and seating depth that works best in your rifle. Which will make you range shooting much more economical, efficient and enjoyable.
I've learned over the years that rifle and load preparation is much more effective than throwing tons of lead down range.
As for manufactures I suggest either Remington or Savage as they seem to me to be the easiest to work on. Plus with the Savage barrels and bolt faces can be changed to be able to also go the 223 route.
Just some thoughts.