A few basic things to start with that do not cost a lot of $$: REMOVE THE J-LOCK shroud, as these have proven over and over to have negative impacts to accuracy. Some varmint rifles have reduced group sizes by 40-50% from this one change, and almost all I have seen or discussed improved at least by 25%.
Trigger adjustment: IF you are not safety minded, then please find a gunsmith, but many shooters can adjust the screws to a safe 1 1/2 to 2 lbs (Use a gauge). THEN use blue Loctite or a dab of your wife's fingernail polish to keep the screws from loosening under recoil and leading to a too lite trigger, or as in this case, a failure to engage when closing the bolt.
The forward stock pressure point Remington often uses may or may not cause any issues. I have several older 700's that shoot wonderfully well, and the pressure points are still intact. Your mileage may vary.
Barrel: Check the crown on EVERY round crown "factory rifle" some are good others not so, and Brownells offers a target crown hand-tool to improve this. Many modern rifles now come with a target style crown, and these are a great improvements.
Also on the barrel, many factory production barrels are rough, have highs and lows and need lapping, and this can be accomplished by any amateur with Tubbs Final Finish kits. While I hand-lap my own barrels, this is not for the beginner. Some tests I have conducted with Tubb's kits showed considerable group reductions, lower SD shot-to-shot, less or eliminated pressure spike induced fliers and far less fouling then before lapping. Given the time it takes for me to lap a barrel, I am leaning toward using Tubbs almost exclusively.
Usually, I begin with these before going on to bedding, stock channel alterations, bolt lug lapping, etc, and depending on the initial results and use for the rifle, it may cease right there.
The 221 and similar lower velocity .224's are often fitted with a 1-14 and even 1-16 twist barrels, so do not begin load development with a boat-tail or Tipped style 55gr bullet or heavier. While some rifles will shoot these somewhat well, begin with the 40-50gr bullets first. If you desire a heavier bullet, then advance to a shorter flat base, lead nose 55. Example, I have an older 222 Rem that has a 1-14 twist, and it will shoot Sierra 63 SMP's into 5/8-3/4 inch groups, but some of the longer Tipped and boat-tail 55's group over 1 inch. The 50's shoot 1/3 MOA.
Also, some rifles shoot better with a fire-formed and partially necked sized case, as often, this helps align the bullet with the bore and reduces case/bullet/bore misalignment in sloppy factory chambers. Some rifles respond better to this than others.
Those are a few lower cost points to begin to test the potential accuracy of a factory rifle, and one can add $$ up from there. Usually, these will make "most" factory rifle owners happy, for the rifle hasn't broken the budget and allows more money to spend on one's spouse and make up for all those days on the range and out hunting. At least that is one theory.