Like Boykjo said, wheel bearing grease. I use "Green Grease" which is a synthetic. I use it on all my trailers, both utility and boat. It will be fine for those gears and can usually be found at any auto parts store (or go with whatever synthetic they have if they don't carry Green Grease). Actually if you want to be exact on what to use, it needs to be NSF food grade gear grease. However if the construction of the gear case makes it impossible for any grease to leak out, automotive or marine bearing grease will work and is a lot easier to find. Make sure to ground the frame as those old motors never had grounds (and neither did houses back then).
As to new plates. The #10 and #12 grinders use the same size plates so you have a lot of options. Stainless steel or hardened carbon steel will work. Just make sure to hand wash and quickly dry any carbon steel items and then hit with food grade silicone spray (like the LEM grinder spray), or cooking spray oil like Pam to keep the carbon steel from rusting. I have both types and I keep my protected carbon steel knives and plates in a zip lock bag so I don't get the oil everywhere in storage. The carbon steel plates are less expensive and work just fine. Stainless will rust so give it protection as well (it can rust, just not any where near as quickly or easily as carbon steel).
I would look for a set of 3/16" (4.5mm) or 1/4" (6mm), 3/8" (10mm) and 1/2" (12mm) to start. It really depends on what you want to make. If you are looking at hotdogs and other emulsified meats, then also get a 1/8" plate (3mm). They also make a stuffing plate which has large holes to act only as a spacer to hold the grinder screw in to feed meat into a stuffing tube in front of the plate. I would avoid using the grinder to stuff, but if you have no other option, it can be done.
Just google #12 grinder plates and you will find them in dozens of locations online and on eBay. Any of the sausage supply websites, websturantstore, Bass Pro, Cabela's, LEM, Gander Mountain, etc... Also if you have a Bass Pro, Cabela's, Gander Mountain, Academy Sports, etc... nearby they probably have them on the shelf.