I will need to think about this over the next few days and read up on it but I think the Savage Arms Axis XP in either .223 or even .308 is a real possibility for the 200 yard range. Online retailers have them for around $320 (Buds Gun Shop even ships for free) so all I need to find is an FFL holder to ship the gun to then transfer the rifle to me and do it for under $25 (good luck with that). The gun actually comes with a 3-9x40 scope which is what I have on my Ruger American Rimfire. I could hypothetically shoot it as it comes, I just have to zero the scope.
The price is just right but from what I'm seeing so far I won't be shooting much better than 2 inch groups on average. I guess that is about what I'm shooting with the Ruger American Rimfire anyway so I shouldn't be terribly worried but it would be nice to be shooting around 1 inch on the regular. The .22 LR would still be cheaper to feed even with inflated prices. I would likely have to replace or work on the trigger to improve the pull; I would likely replace it with a Timney. Boyds has replacement stocks for the Axis so hopefully that would be a good option later on. The barrel is 22 inches which is around what I'm looking for and has a 1:9 twist rate for the .223 Remington version. This is good because it should be able to stabilized the 70 grain bullets I'm looking at using for target. The .308 version has a 1:10 twist rate which Berger Bullets says is suggested for their 215 to 230 grain (yikes, that's heavy for 308). The Axis has a 3 round magazine for the .308 and a 4 round mag for the .223 version; as if I were concerned about that.
As an alternative, the Ruger American's trigger is already pretty good and is adjustable. I already have the rimfire version which I like. In .223 Remington, the American has a 5 round magazine and a twist rate of 1:8 which is better for the heavier 75 grain bullets. The .308 version also has a 1:10 twist rate. The price for the Ruger American in .223 Remington is just around $25 more than the Savage and I can't find it on Buds but they do have the .308 version for $352 with free shipping. Impact Guns has it in .223 for $344 with around $10 for shipping; its $334 for 308. I would still have to buy a scope AND rings for the Ruger but the scope and/or rings on the Savage may not be all that great but it would be a start. Both guns have similar accuracy from what I've been reading. The stock on the Ruger isn't bad but it has these interesting V shaped bedding blocks that meet up with cuts in the receiver. I would have to use those blocks if I were to swap out the stock. This isn't a big deal but the Savage appears to use a more traditional system.
I'm more inclined to go for the Ruger American over the Savage Axis XP for the adjustable trigger and the twist rate (assuming I went for .223 Remington). However, I would HAVE to buy a scope for the Ruger where the Axis already has one. This helps with the upfront costs. I assure you that I would replace the Axis' scope at some point. Even if the Axis XP didn't come with a scope, it's still cheaper to begin with, making it more appealing to my wallet but I have a 5 to 6 lbs trigger pull which is nuts; the American can adjust to around 3.5 lbs from the stock 5 lbs.
I may sell my S&W M&P 15-22 since I don't use it much, to try to come up with part of the money. I think I will try to talk myself out of this silly idea over the next few days.
Update: I think I've settled on the Axis and most likely in .308 but I really like the idea of a .223 bolt action for the low recoil. I won't likely be using this for hunting but I also think .308 is just too universal to say no to. The smart play is .308 Winchester but .223 Remington's cheapness and low recoil is just so attractive. I will have to either dig deep or straight up buy one and live with the decision. It's not like I plan on doing any hunting anyway. Once I choose a caliber I will decide on whether to do this or not. I should just say no.
Update: So, I've settled on .308 Winchester for one very specific reason. The Axis is likely not going to be the sub-MOA rifle out of the box I want it to be. I will likely be shooting 1.5 to 3 inch groups which means that this rifle NEEDS to have another purpose. Since I won't likely be able to use it for precision bench practice it will need to have another practical reason; hunting. Even though I won't be doing much hunting, having the ability to hunt deer is the main reason to choose .308 over .223 in this situation. If the rifle was capable of shooting sub-MOA all day, everyday then I wouldn't mind having it specifically for precision bench practice. So there you have it. The Savage Axis XP in .308 Winchester will be the Phase 2 rifle build. I will run the stock scope until I can't stand it then buy a better scope (unless the stock scope doesn't suck). Now to figure out if I should or shouldn't make the purchase this year.