You're quite right: a W in front of the serial number does indicate a Winchester-produced rifle. Winchester was the first of the three plants to get into production, they did much of the tooling for Remington's two plants AND they made the first 300-odd pre-production rifles which went to England to prove that Americans really could build a British rifle properly, even if it had German ancestors.
You appear to have a complete bareled action and needing only the woodwork. Woodwork is available, as are the nose cap/front band/bayonet cap (all one part), middle band, buttplate and so forth. The one part you will have trouble finding is the ring which sits atop the chamber and holds the rear handguard in place. They are not terribly expensive but they can be hard to find. Gun shows are a decent source of parts for this rifle; I have seen buttplate assemblies a low as $2....with the butt trap complete and installed. Try Trade-Ex or Marstar (both site sponsors) or parts.
You HAVE the hardest part of all to find: a good barrel, already installed.
On the market today, likely something like this is "worth" $150, and that is silly. Pop in another 100 or so for the parts you need, and you have a nice $350 - $400 rifle. OR pick up an action and try to have a very darned good long-range rifle built.... take your heart pills...... then check the price.
In decent condition, this is a 1-MOA rifle. I have a couple here which will do that, one in .303, the other in .30-'06. I have 2 more in .303 which are projects-in-progress, including one of the first prototype rifles built by Winchester, and I have every confidence that they will perform just as well. That Enfield-rifled barrel just doesn't know when to quit, espcially if you feed it FLATBASED bullets.
You have a fine Project, friend. Get the parts, finish her and take her shooting. You will go a long way to find a BETTER rifle under 2 grand, believe me.
Hope this helps.
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