I have the exact model as you, and if the part # by S/N is the 106648 it is the HS precision per their web site. I just verified mine by S/N and it is that P/N and is the tactical stock. HS web site, I think lists it as the pst114 or 112. Suffice it to say it matches Savages web site description and picture to a "T".
As for the stock, some don't like it, but it fits me perfectly in LOP and palm swell. Heck, the first 20 rounds down the pipe on mione brand new had me grouping two 5 shot groups roughly 1/2"x1/2" when I was sighting in. It took exactly 2 3 shot groups with slight corrections then the 2 5 shot groups. Sent the last four rounds down range just for grins to finish off the box and it was still nuts on.
Of course, when I got home to clean, is when I found a crack in the bolt head. Within 30 minutes, I had a return tag from Savage, shipped it off, and just learned today it is in route back with new bolt head, head space checked, function tested, test fired and cleaned. Savages customer service is fantastic, and the turn around time is phenomenal.
Should have it back next week and will update on a thread I started about the bolt head crack discovery. Enjoy yours, it is a fantastic rifle and well built. Oh, just FYI, check your action screws for torque. I ran mine @ 60"/lbs per previous HS suggestions (actually they say 65) and will say that Savage had them at about 35. See what works for you, all rifles act a bit differently.