If you're looking at older push feed and even some early controlled round New Haven Classics from Winchester in the FW Model, wood will definitely be the stock material.
Most New Haven Winchester rifles are good rifles if you can find one at a decent used price. Some of the last ones put out from New Haven by USRA were sketchy and hit and miss as far as good quality went. The union workers there were told that the factory was going to close and quality went out the door the last few months of production. Check Winchester serial numbers lists for years made and look the late-stage New Haven rifles over carefully.
Ruger Hawkeye rifles are good also. I have a sporter weight 220 Swift in the Hawkeye model which is an excellent shooter. Either choice would be a good choice.
One newer Model 70 with a synthetic stock and stainless metal is the newer Model 70 Extreme Weather Model. I have a couple of them in 30-06 and 7mm-08. The 7MM-08 is built on the short Model 70 action and is a very nice rifle, IMO. Both of my newer EW rifles shoot extremely well. Any of the newer post New Haven rifles are good quality rifles. The latest ones are actually assembled in Portugal, but they are of excellent quality also, as are the post NH rifles made by BACO or those made in South Carolina.
Again, you can't go wrong with either choice of Winchester or Ruger, IMO.