Took a while to get back to this. Got some pics. Scotch Brite and oil? Anything I should check in the way of bearings, etc, before I turn it on for the first time?
Oof!
People saying not to use abrasives and then recommending scotch brite cracks me up. Scotch brite is plastic imbedded with an abrasive.
Also, while WD will work, it lubricates. You want kerosene or at least diesel fuel, these will let the abrasives cut and make the work go quicker.
I would fully disassemble that, start off removing the heavy rust with 230 grit, and finish with 400-600 grit all being done slowly and by hand with maybe a paint stirrer to back the paper up for the flat parts.
Mix up some "Eds Red" (look it up) and soak the chuck and tailstock along with other stuck parts and let that soak for a week. By soak I don't mean you have to submerge the parts, just wet them anytime you walk by.
Then once you have everything shiny, fully clean it with hot soapy water and dry with compressed air and coat with WD to prevent flash rust, then reassemble.
Been doing everything from automotive engine rebuilding to tool and die for 40yrs, and abrasives are always used, albeit with great care and in the proper fashion. The key is the item being disassembled so as to allow proper cleaning before reassembly.