Savage plastic stocks?

I stumbled upon an old Stevens 200 in 22-250 with a grey tupperware stock. (good shooter) I really do not like how much that stock flexes so I got on ebay and found a savage take off black plastic stock from what must have been a varmint rifle. It has the wider thicker beavertail forend, pillar inserts for the mounting screws, blind magazine, short action 4.4" spacing on the screw holes and top bolt release. I assume that the wider heavier forend will be more stable than the standard stock I am taking off?

I've never had a rifle with one of those stocks so I can't speak to their stiffness, but I do know they only came on rifles fitted with heavy barrels so if your Stevens 200 is still wearing a factory sporter barrel you'll have quite a gap around the barrel. Won't hurt anything, but aesthetically it will stand out like a sore thumb.

They are not any stiffer than the sporter stocks, but they will fit a front bag a little better.

I have a Mod 11 trophy hunter. It started life as a 204. I have put 223 and 243 barrels (sporter profile). I have found that despite the synthetic, flimsy, tupperware stock the accuracy is very good in all of the calibers. Go figure. I have had thoughts of getting a better stock but I think that all I will improve is appearence. The synthetic stock is very light weight but seems to absorb recoil making the rifle very handy and a pleasure to shoot.

I have two Savage centerfires with synthetic stocks, however, they are the accustock version with the aluminum "bedding rail" inside. IMO they are pretty firm and very accurate. If you can find one of those, and if it will work, I would go that route.

I had one of those Savage factory stocks on my old 10 FP .308 that I got in 2007 or maybe early 2008.
After shooting it for several years and wearing the barrel out at about 6500 rounds, I had Savage change the barrel to a fluted, suppressor-ready, target barrel.
When I got it back from Savage with the new barrel, I changed the stock to a Bell & Carlson adjustable stock that had an aluminum rail.
It was made for the hidden magazine of the 10 FP.

That stock and the new barrel improved the rifle's accuracy by about 45%.

It turns out the factory stock on the 10 FP was a bit too short for me and the adjustable stock made the fit perfect.

Your Stevens probably has the bolt release on the right side of the action.
If so, an Accustock won't be an option since they have their bolt release in front of the trigger guard.
The Accu-stocks, available on many Savages, have aluminum rails and are very stable.

Most stocks available for Savages from third parties are made for receivers with bolt releases on the right side.

I have 3 Savages with Accu-stocks and they don't need replacements IMO.

I have two 2 other Savages with bolt releases on the right side of their receivers.
One of the non-Accustock rifles has the adjustable Bell & Carlson aluminum rail stock with a hidden mag and the other came with an HS Precision aluminum rail stock with an detachable mag.

I'm waiting for my Bell & Carlson to show up for my Hog Hunter .308. Currently, I have an Accustock that has been modified to allow for the top bolt release. If your rifle has the 4.40" screw spacing, this might work for you. It's plenty stiff and it has the digital camo pattern on it. It also has the inletting for the factory detachable center feed magazine. You would have to buy the bottom metal parts from Savage. Call Savage tech support and they will tell you if this will work or not. I'll let it go cheap once it's off. Let me know if you're interested.

I took the sporter stock off of a model 10 and replaced it with a 12fv stock (beaver tail stock). As Jim stated, it looked a little funny, but there was plenty of room between the barrel and stock. I also epoxy bedded the action and the rifle shot nicely. Better recoil pad and more of a base for the sand bags as Sharpshooter noted. You mentioned a Stevens 200, but the look and feel will be the same.