My Marlin tube fed .22 is a tack driver and was under $200 at bimart.
I don't think with a 10/22 you could measure any substantial accuracy differences between a chrome moly barrel and stainless. Most short range benchrest rifles are built with stainless barrels and will shoot with incredible accuracy, so I don't think there is any merit in the speculation you heard.
As for accuracy, most 10/22 rifles are far from what I consider an accurate rifle. Very enjoyable to shot, just don't expect very small groups. You suggest 2moa but don't specify a distance. My experience with 10/22 rifles is they are hard pressed to shoot 1 inch groups at 50 yards and a two inch five shot group at 100 yards is pretty darn good. You might do better with high quality ammo, but you can only expect so much accuracy from a pressed in barrel.
You can dump a lot of money into a 10/22 and improve accuracy some what. I ones I've shot that were customized would shoot better, but only marginally so. I like 10/22s for what they are...extremely fun to shoot tin cans and blast away at targets. If you are interested in accuracy, I would lean toward a Savage or CZ bolt action rifle.
I used to have one of these 22” barrel models and it was really accurate (meaning easy to shoot it accurately) using iron sights. I think u can still buy them at Walmart but am not sure on that. They aren't that expensive. The only thing I did to mine was polish the receiver for looks only. The receivers are aluminum but painted aluminum color. So you can remove the paint and polish with a dremel to have polished aluminum look pretty easily and it matches really well with the stainless barrel. I don’t like that painted aluminum look personally.I am looking to add a 10/22 to the stable and I would like to know what I can reasonably expect for accuracy. I am looking for a stainless carbine barreled model. With ammo it likes could I expect 2 moa? I have heard speculation that the stainless barrels are not as accurate as the blued. Is there any truth to this? Any thoughts on this would be appreciated.