I think your savage 12 will shoot pretty well for you. I'm a Remy guy, but I think the Savage shoots better out of the box. A 30" bull bbl will be HEAVY. I'd be surprised if it could make weight without heavy fluting (then you might as well get a smaller contour). A friend of mine, who shoots far better than me, has told me repeatedly that a 28" bbl is ideal for Varget and similar burn rate powders. If you must have the bull, you might consider going to a 28". It won't be a huge difference, but it will save you some weight.
I'm no expert on this matter, so this may be worth exactly what you paid for it, but.... If I were going through the trouble and expense of rebarreling a rifle, I would not go with a prefit. I know several guys that use Savage actions for their TR rifles, but not a one them uses the barrel nut. Several of these guys are world class competitors (I am not. I'm just that guy out there having fun and NOT cussing up a storm.) I know Criterion makes a quality bbl, but you could easily step up to a Krieger, Bartlein, Lilja (current F-TR world champ shoots Lilja), or any other premium maker for very little. I seriously doubt you will regret spending a little extra $$ having a bbl fitted and your action trued. I'm just telling you this because I spent SOOO much $$ doing things in a manner that was not the best way of doing them, until I met a very talented gunsmith who told me what to do to build a great rifle.
FWIW, I am building a REMY W/Lilja NBRSA heavy varmint contour 3-groove 1:10" (finishing @ 28"), MCM A5 adj. (great stock, but not for F-class. expensive mistake), Sightron SIII 8-32x56 LRMOA, Farrel rings, and NF base. I'm hoping to finish out at around 17.5lbs