Well, two ways to go, I think. The Stevens 200 build that TacticalPanda listed above is a great way to end up with a really nice rifle immediately. The 200 is effectively a non-accutrigger Savage 10 action. If you're going to replace the stock, trigger and barrel anyway, why spend extra cash on Savage parts you weren't going to use? There are a lot of these out there used, they were cheap when new, and they are a great spot to start from for a right hand build. (Don't I wish Stevens offered lefty 200s...) The B&C Medalist is an interesting looking stock - but I haven't seen one in person yet. I want to, because I like the look of the stock, and I'd like to see if the aluminum chassis would get in the way of converting one to left hand. Not to pricey, either.
Or, if you can track down one of the Savage 10 FP series in 308, you can shoot right now, and upgrade trigger, barrel and stock in the future. At that point if you decide to press on to another caliber, just change the barrel. (Well, and maybe the bolt head and mag box, depending on which caliber). You'll also get to shoot it before you start picking upgrades, which might influence what you want to change. The factory Savage barrels usually shoot pretty well out of the box, too.
What it may come down to is what's available in the current gun buying frenzy. I think the biggest concern with building on a Stevens right now is parts availability. Of course, if you can't find a 10 FPxx either, it's kind of a moot point. Would you be happier with a factory built rifle ready to go out of the box, or does the process of choosing and finding each individual part of the rifle sound like more fun? Total builds never seem to run totally smooth, although the end result is usually worth it. If you get the factory rifle, you can order a Rifle Basix trigger, and when they tell you they're on backorder until the 5th of Whenever, you can keep shooting until they ship your upgrade.