Ahhh there's a few true classics on that list!
The Savage 99, it's on my list of "must haves" and of course it will have to be in 300 Savage. They mostly were typical Savage, so-so finish, cheap wood but they did what was most important... they were tough and shot well. Rare and premium grades I've seen bring over $3k but those are EXTREMELY rare cases. The typical "grandpa hunted with it for 40 years but it's still a nice gun" types will usually bring $350-$600. BUT this price is going up steadily, there's a sudden surgence of interest in these guns lately!
The model 12, hell what can be said about arguably THE most reverred shotgun in history (I think it's a toss up between the 12 and the A5!) My grandfather got a Stevens m12 copy when he was only 12 years old (and it was second hand then!), that gun is now in my dads possession and he was given STRICT instructions to hand it down too me one day. The other night my dad came over (lives 5 hours away) saw my new gunsafe and insisted I get that gun early so as to protect it in the safe!!!

I've seen rusty old "broomstick quality" m12s bring $100. But typically the 90%+ field grades will bring $400-$800. And again, there are many exceptions (especially like pigeon grades) that will command nearer too $3k+.
The 97 as was said, ok if you like that old style. Personally I think the m12 is Ferrari compared too a Model T like the 97. But hey it's whatever floats your boat! Haven't a clue on their value.
Rem 11: I think alot of people just don't know the history of this gun. They are NOT copies of Browning's A5, they were actually built for Browning and imported by Remington. Browning had a fallout for a few years with FN so he couldn't get his A5 imported, the friendly folk at Remington knew a winner when they saw one so they gladly imported them for Mr. John Moses himself! They are good guns but being so old they are scarcely in good condition and because they don't have the "beloved Bs" on the side (Browning and Belgium) they aren't nearly as desired as their A5 cousins. "Bedposts" condition 11s can't be given away. The typical field grade in %75+ condition might bring $200-$300. The nicest ones I've seen did good to bring near $500. They are still there for the stealing right now! But interest is slowly coming up on these guns as well.
Model 10: I guess I know the least about this gun on the list. I cede to others.
A5:...... SCCCCCCCCCCCWING! THIS is my personal most favorite shotgun of ALL TIME and if they still built them I would buy a new one every year! I think they were offered through Browning's Custom Shop until just the last couple of years, but if memory serves me correct (which it rarely does) the starting price of admission was in the $4k range! [:@] I plan on owning several in the future (already have a Sweet 16 in my grasp) and would actually like to get a late model Stalker version (yep they had synthetic stocks) with a 26" Invector barrel to shoot heavy steel at ducks with. And a plethora of various grades for occasional wing shooting, collection and ogling over!

In all honesty there are a whole host of "technically better" autos out there for hunting with. But the A5 is a historic and pure too the wingmen as the ol 30/30 leverguns are too us deerhunters. We accept their limitations yet still choose them from time too time over much more modern equipment. I have seen A5s bring $150 for rusted out "doorstops" too as much as THOU$ANDS of dollars for premium grades in like new condition. The regular field grades and lightweights in 90% or better condition typically bring in the $500-$1k range.
Hope this helped,
RA