All of the previous posts hold excellent advice. As usual, I hold with a slightly different line of thought.
The rifle you have was bought for a different purpose than what you want it to do now. Does it do the original purpose well? Are you completely done with that purpose?
I would begin by seeing if I can develop the skills and consistency needed for the new purpose with the rifle as is. Proficiency with the new purpose comes from the shooter, and not the rifle.
Precision can come later, but will not come without the proficiency, regardless of the equipment.
That wear and tear you accumulate in this initial process is better accumulated on the old rifle than on the optimized rifle. Once you can be content with your basics, that's the time for upgrades, and the proper upgrade is a complete rifle; one that is better suited from the get go.
Start that process with something more basic, like a Varmint rifle. It can be a used rifle, and the for sale section here is a good place to look.
If new is your bottom line, start with
Savage. Their variety of rifle models is huge, and I suspect you will find something there that suits your 'first LR rifle' needs very well. If they don't have it for this stage of your development, you may well be looking for the wrong rifle.
Meanwhile, the original purpose is still well suited to the original rifle.
This approach may appear slow, but it is also deliberate. Getting the process right is usually not compatible with speed. Buying into the upgrades will not necessarily deliver any improvement; one cannot buy accuracy, one can only buy the means to attain it.
Additional time can be useful, as it allows one to spread the expenses out over a more reasonable time. Moreover, I think the best investment in proficiency is ammunition, and less so, equipment.
My preferred aftermarket stock maker is McMillan, and for the barrel, I go directly to Lothar-Walther. With upgrades, cut no corners.
My first investment would be in an adequate, but not exorbitant, handloading capacity.
My second would be a Savage .223 Varmint rifle. Take a look at the Axis Heavy Barrel .223, for under $400. The Axis II Xp has DM, Accu-Trigger, and a reasonably decent Weaver 3-9x40 Kaspa Scope for about $100 more, but lacks the heavy barrel. That might change.
You can buy .223 ammo a lot more easily (and probably cheaper) than .22LR these days, and it's not especially expensive to reload it either. .223 is reloadable, .22LR is not.
I'm buying TulAmmo 55gr .223 in the 500rd spamcan, and collet pulling everything down to components. The steel cases are Boxer primed and reloadable (at least five times so far, do
not try for max loads), and the resulting loads come out to about a quarter apiece.
It's not match ammo but it's at least as good as factory varmint loads (once one does the necessary load development). Aside from chamfering the inside of case necks (initially, to eliminate shaving bullets during seating), the reloading process is identical to using brass cases.
For the second and successive loads, I'm using my match load recipe with 69gr and 75gr Match bullets, with no visible performance difference from brass cased loads (my match loads are nearer the lighter side than the hot). So far, primer pocket growth has been a non-issue, and if a case can't be recovered, it's no great loss.
Greg