For the most part, stainless barrels have shown a greater potential for better accuracy over steel barrels, but that's old school mentality. It doesn't take into account new manufacturing methods, for either barrel material. There are steel barrels out there that are highly accurate, and even mass produced. As long as you get a barrel from a reputable barrel manufacturer, it will shoot very well, no matter what it's made of. The definition of "reputable barrel manufacturer" will typically not included budget barrels that you find on sale for $99, either. I'm talking about companies that only make barrels, and few other items...
16" will get it done. That's plenty of barrel. Depending on the weight of the projectile in the loaded ammo, you'll have enough power to make clean kill shots at 500. Example on loads, 178gr Hornady BTHP projectiles loaded to 2400fps. That's 1100 foot pounds of energy at 500 yards.
Lot's of variables in your questions,though they might seem like basic questions. Tons of answers available.