Ya, Millwax has a solvent component to it. The odds of it hurting your playfield are probably really minimal, but a lot of people stay away from it for that reason. I like a good solid carnuba wax. Any wax that is liquid and in a bottle, I figure is primarily a "cleaning" wax, and not what I want.
I'll let Novus 2 do the cleaning, then follow with as many coats of wax as I have the patience for. If you have a Harley dealership nearby, they often stock Novus (good for helmets apparently).
So pretty straightforward - clean with Novus 2 (a liquid type material), buff until clean and shiney. It should look pretty good at that point. Put some coats of wax on top to protect it. Clean/change your balls if you haven't done that yet.
You'll ultimately want to take off most of the plastics to get down into the nooks and crannys and also to polish the plastics (use Novus 2 for that). But if that's a little intimidating to start, just do something easy like a sling. Strip it down to the playfield (easy to do), clean everything up (it's amazing how dingy the undersides of the plastics become) maybe new bulbs and rubber and reassemble. The star posts probably have old gunked up wax or Novus in the details - pull them off and clean them up with a toothbrush and your cleaner of choice. Put everything back together, stand back and admire how much better the one you just cleaned looks than everything else.
And if you are like me, that will drive you crazy and you'll start pulling all the other stuff off the playfield to make it shine too. Have fun!