A stock Remington 700 or a Stevens 200 with an aftermarket barrel, they're awfully close in price. Which will be the most precise with factory ammo for a beginner? (Or is there a better alternative?)
Savage w/ accutrigger and a HB with whatever stock floats your boat. If the goal is the upgrade stocks in the future, do it now. Aftermarket stocks are not always easy to get and can get real pricey. One of the few times, factory set up is cheaper in the long run.
Within your budget, the Savage 12FV (or whatever it is called now). BVSS is about $150 more but it will offer you SO MUCH more that is makes a worthy upgrade.
Accutrigger is one of the best triggers on the market out of the box and will serve you well for many years. many never 'upgrade'.
Rem X mark Pro is not exactly the most desired trigger group on the market.
223 9twist will shoot both factory and handloads very well. 1/2 min is not out of the questions with the factory barrel and handloads. 223 varmint ammo is some of the most accurate factory ammo you can buy. Win white box 40gr bulk stuff usually shoots sub MOA in most factory rifles.
When you start reloading, you can put in 75gr Amax or Bergers and shoot as far as you want.
Most important is get any factory rifle bedded properly.
The Savage will allow you to quickly and inexpensive change whatever part you want down the road. But if you get into handloading, you may find a 12 BVSS all you will ever want in a LR target rifle.
At least until you burn out the barrel 5000rds later.
Enjoy your quest....
Jerry