Hi everyone, I've just acquired my first bolt action rifle and it's a used Savage Model 10 in .308, but I've got a few questions about it I couldn't figure out with a day of googling, so I figured I'd just ask here. First off, I'm not quite sure what model I have and whether it matters or not, and I've also got a question about the stock.

The barrel I've measured at 22", unthreaded with a recessed crown, it's matte black and feels similar to a QPQ nitride finish. The engraving on the barrel says "SAVAGE MODEL 10 CAL .308 WIN." and has "A302" next to it in small letters as well as "A7" perpendicular to it, in case that's relevant. It's got a picatinny rail base on it (not sure if it's factory), the bolt release is on the top/side, and it has a double-feed blind magazine with what appears to be a 4-round capacity though you could force a 5th one in there without too much fuss. It has an Accutrigger and the stock doesn't have any distinguishing markings on it but it's fairly flimsy and plastic. The action mounting screws are about 4 and a quarter inches apart.

Beyond knowing which model I have, I'd like to know if it'd be advised to change the stock out? The barrel is fairly well free-floated all the way down, but at the farthest end towards the muzzle, the stock has a significant amount of flex and it doesn't take much lateral force at all for it to contact the barrel, which I would think isn't ideal. It's also not quite centered, with the barrel being closer to the left side of the stock than the right by about twice the length. With the picatinny rail base, I've simply stuck on a scope I already had with a quick-detach AR-height mount at 1.47" but this is quite a bit too high for the standard stock. I've taped on some foam to act as a cheek rest and it works fine, but between this annoyance and the flex near the muzzle end, I'm thinking of swapping it out for something with an adjustable cheek rest and a stiffer construction.

So, to cap off, which specific model do I have (and does it matter) and where should I look for a good stock?

One last note is that the rifle comes from a family friend, and he's got four rubber o-rings about an inch from the end of the muzzle that he claims helps with accuracy. I've shot some Federal GMM 168s and 175s through it and it's ridiculously accurate by my standards, with every group well within an inch at 100 after an hour's session at the range, so I don't think it hurts the accuracy and as such I haven't removed them, but is having the o-rings normal? I've never seen or heard of such a thing but my only firearms experience before is with carbines and handguns with more of a tactical focus than anything really geared for long-range or accuracy.