You're talking maybe $10 of wood. The labor to shape the wood is a bargain if you find a hobbyist (retired guy with small wood shop, as example). The glass can be gotten at a glass shop cut to size for about $5. A local framer will cost you about $35-50, probably the low end.
I make my own frames and have many aviation art works. Your job just screams for a ma & pa small shop. If it were me I would choose a simple profile with rich cherry stain and no matting.
A simple frame works best with the long rectangle and is not overbearing to the subject. For mounting the litho in the frame, clean cardboard of course for the backing. If worried about the cardboard sticking to or bleeding through the litho, place tissue paper between the two. No adhesive or tape.
1st Pic: #460 is what I'm thinking.
2nd Pic: This is also simple but has the fine detail on the outside edge.