Read much of the information at pinrepair.com- This individual has restored a ton of games, knows what they are doing and have published free illustrated guides etc. Also, look up this on YouTube. There are at least two people who regularly publish video how to for what you need. Questions after you have some idea what to do will probably be more interesting to answer. For now, just read, do your home work.
PLAY FIELD
Clean with basically no water or at best a damp (like very very dry) rag or wet with windex. Test in inconspicuous spots first. Then, try some Naptha which can help strip old wax. Then Magic eraser with 91% isopropanol but you probably need to take the entire play field apart to do this effectively so enjoy the project, its great for tinkering.
CABINET
Wood chips can be filled with pretty much whatever you like if its on the cabinet and then you need to blend colors (I would use spray paints and spray in a cup to blend two close colors). Remember, order of paint on cabinets was always Base color (typically white) first- then the splatter/web black fleck... then typically you need to look at the stencils to see overspray patterns but the stencils were last and over the splatter and you should try to figure out which one was sprayed first as it slightly changes the way the overlap looks... if your going to cut stencils and repaint parts you need to know this... (done this, it should not be your first choice). Better, match the base color and both stencils with some spray paint (IMHO DO NOT USE double coverage paint its TOO dark you want to see though it a bit)... patch the wood and sand flat carefully (only the patches) then probably run down the cabinet good to remove paint that its going to fall off with the brush, and simply go over all the stencils and scratches very very carefully.
Broken Arrow, OK
