Kenny,
either the 12F in 6BR or the 12 BR in .308 would be a good choice. Like others above, I'd personally go for the 6mmBR model. However, you may want to think a little as to what you might want to compete in subsequently and over what distance(s). If you're thinking shortish range 'factory sporter class' benchrest or F-Class, the 12F in 6BR is a very good choice. If you fancy mid and long range BR or F, the 12F in 6.5-284 would be more competitive (but at the cost of higher reloading costs, more recoil, and a relatively short barrel life). You can always start with the 6BR of course and rebarrel to anything that uses the common 0.473" dia. case-head later (.308Win, 6.5X47L, 6.5-284, .284Win to name four popular cartridges in competition) that suits the discipline you choose.
One thing to bear in mind if you fancy having a go in F-Class is that there are two classes - Open and F/TR (often called F-Class Restricted). Open allows any calibre and cartridge up to 8mm and most shooters use a pedestal front-rest. Performance and good ballistics (alongside good accuracy) rule this form of shooting, hence the provision of the 12F in 6.5-284 Norma calibre. F/TR is restricted to .223 Rem and .308 Win and pedestal rests are not allowed, an attached 'bipod' used instead. You can screw in a stud and attach a bipod to the F and BR models, but both have wide flat-bottom forends designed for sliding on a front-rest. The Savage 12 F/TR model has a narrower forend designed for bipod fitting, and is a good starter model for F/TR shooting out of the box. (Team Savage members using selected but otherwise out-of-the-box 12 F/TRs were placed 3rd 9th, 10th and 13th in F/TR class in the individiual matches in the F-Class World Championship meeting at Bisley in England last July, and also formed half of the winning 4-shooter US F/TR team in the team event.)
Incidentally, the wide forend on the F and BR models does involve you in some extra costs to be considered. You will need a reasonable quality front-rest that takes or comes with a top with a three-inch wide bag and has to be sturdy and steady enough to cope with a long and heavy rifle. The better Caldwell rests suit, but their tops are not as good as those from specialist benchrest rest providers such as Sinclair, Bald Eagle etc.
In UK BR Assoc 'factory sporter' class at 600 and 1,000yd benchrest shooting, it's a near complete line-up of 12Fs in 6.5-284, hardly a Remington seen these days, and some of these rifles are real tack-drivers, Phil Gibbon setting a new UK FS 600yd small group record last Sunday with one.
In any event, whichever Savage model you choose will be a good entry into precision and competitive shooting, and there is a good resale market for these rifles if you decide to change to something else in the light of experience, as well as being very easy to rebarrel and/or reconfigure if needed. Go and register on the free forum section of the huge Savage Shooters website that has vast amounts of information about these rifles and also many links to specialist Savage rifle 'goodies' suppliers.
http://www.savageshooters.com/index.php
Oh, one final thing. I seem to remember that the 6BR Savage 12F was made in 1-12" twist and short-throated (for light bullets) as well as the 1-8" twist / long-throat 6mmBR Norma form until recently. Unless you're going to restrict yourself to short-range benchrest, make sure you get one with a 1-8" rifling twist barrel. That lets you use the heavy and more ballistically efficient 6mm match bullets in the 90-108gn range that are better suited to 300yd and upwards ranges.
Good shooting,
Laurie,
York, England