Any particular reason for .308? Just asking to see if you're stuck on that caliber for a reason? I do have several .308s of different stripes from compact carbines to long heavy barreled rigs that almost need wheels and a few in between in the cabinet right now myself.
In the model 12 I prefer the 22-250 in a heavy varmint style configuration with the laminated stock stainless fluted barrel etc. they are pretty and functional. I think it would do fine for the use you describe, range and paper to 200 and out to 500. I have a 12BVSS that's stupid accurate in 22-250 and it's much more economical to load for than a .308.bullets are about half the cost of .308 bullets and I save quite a few grains of powder per cartridge as well also very little recoil and those little bullets are really cooking with a laser beam trajectory. The ballistic plex reticle on my Burris 4.5-14x matches the trajectory nearly perfect making the setup really easy to use and enjoyable.

Just like the model 12s the model 10s come in many configurations as well. Everything from pencil barreled hunting rigs to scout style carbines to heavy barreled rifles with barrels from 20-24" and in as many calibers you can think of. As far as comparison they basiclly all use the same action as Roscoe pointed out.

Weight and barrel length usually aren't as much of a concern for a bench toy so I'd go with a 12BVSS. One of the beautiful things about Savage are the factory provided extras like fluting etc. that come on their reasonably priced rigs. I have a couple of model 10/110 LE rifles that I've picked up through the years that are fun and shoot very well but there is just something I love about the 12BVSS from the bench.
Oh yeah and when pricing your rifle remember to factor in good bases, rings and glass. These necessary extras can push the price up quickly and significantly and you're not doing yourself any favors without decent products.