The hinged oven should have a number on the bottom...2568.
They also made a 2578, that I believe was prior to the handle style change on the hinged ovens. The 2578 has the wire bail style ears, but came with No wire bail handle and has a hinged lid. I dont think the 2578 is in the book, and you seldom see one. If I remember correctly, the #2578 came with a standard hinged oven lid, not a skillet lid. Both in chrome or plain cast iron.
I have always liked the looks of the hammered finish Griswold, and a nice set to own is the #2058 hammered hinged oven ( Page 149 red book), and the Hammered hinged skillets, regular and deep (page 135 red book). . The #2098 lid works with the oven and both skillets. And they all came in iron or chrome finish too.