DTE light or medium oil. DTE = "Dynamo, turbine, engine", a designation that is still in use and predates the automobile, but is still used for powerplant and industrial oils. The modern equivalent is an ISO 46 or ISO 68 oil. DTE oils are straight weight with only an anti corrosion and anti-foaming additive (for use in gearboxes and hydraulic systems). ISO 46 is about a 20 weight oil, and is commonly used in machine tools as well as in tractor and heavy equipment hydraulics and gearcases. Tractor Supply will carry this oil as "tractor hydraulic oil".
Put some of the oil on a rag and apply it with some elbow grease to your vise. Some of the accumulated grunge will come off, and the oil will shine and preserve the vise. Why take a classic vise with a patina from good use and polish and paint it ?
Old machinist vises got a particular patina from years of use, and never looked "spit shined" or glossy with paint. Often, they were a kind of dull black when sold as new. Your vise is in good condition, does not look to have been abused, and has normal wear for an old classic vise. IMO, it will look better if you just wipe it down with an oily rag and leave it as it is. A vise is meant to be used, and in use, the paint (if it had a slick and glossy enamel job) will soon be worn off the tops of and ends of the jaws from work such as bending stock in the vise or from the chips resulting from filing, tapping, threading, hacksawing, and the various cutting oils used for some of that work. My own machinist vises wind up with the jaws magnetized from a lot of the filing I've done. Filing in one direction can set up "domains" in the iron and steel and cause the jaws to magnetize. Handy to hold small steel parts, a pain in the a-- other times. I give the jaws a smack with a chunk of bronze and a steel hammer to demagnetize them. The jaws on my machinist vises are worn bright across the tops and ends for the work I do in the vises. I'll admit to painting a 4 1/2" "Simplex" machinist vise back in 1982 with gloss gray enamel- I had built a work bench out of steel pipe and angle iron, and set a piece of steel plate into the wood top to mount the vise. Being in a painting mood, I painted the welded steel bench structure, and painted the vise. Most of that paint is long gone from use. Millions of steel and other metal filings have rubbed on that vise, and I've cold-bent a lot of steel for various projects in that vise. My attitude is my machine tools and shop tools are to be used, not turned into a museum or similar "objet d' art" (or however it's spelled).
Get an oil can, put some ISO 46 (aka: DTE light) in it, spritz some on a rag and got to town on your vise. Incidentally, a few years back, on a metal pickup day, I spotted a nice 3 1/2" Athol vise in someone's trash along the roadside. It turned out the vise was missing a kind of "garter spring" which fit in a groove on the vise screw to keep it from turning out of the moveable jaw. I made a collar out of some scrap steel bar, tapped it for some socket head setscrews, and the vise was good as new. I gave that vise to a buddy, and he's been using it ever since. I tend to to with making things work and work well with what I have at hand rather than trying to "pretty things up" or "restore" them. As I said, my attitude is tools are meant to be used. I liken it to some people who, truth be known, look quite good with the wrinkles and lines that life's experiences have put on them. When they start resorting to the paint and putty and body work (aka: hair by Krylon on men who would otherwise be gray, or women who have had one facelift too many) the effect is ridiculous and makes them look far worse than if they'd just aged gracefully. Years ago, a fellow had an antique Winchester saddle carbine. I forget the model, but it had the octagon barrel. It also had had the saddle ring. This joker decided to restore and improve on that old Winchester. He took a hammer and blunt chisel to the shackle with the saddle ring, attempting to cut it off flush with the frame. He took flint paper (woodworking sand paper), and sanded the barrel and all else with it. He then took urethane finish and slopped that onto the stock and got some of the urethane into the action and onto the frame. It was an abortion, and I wanted to save that old Winchester and perhaps bring it back to some kind or good condition.
As luck would have it, this joker got his girlfriend pregnant and needed cash, so he sold me that Winchester for small money. I took it to a gunsmith, and he had a fit when he saw the carnage this joker had wrought with his "restoration effort". I traded that Winchester straight across for a 1950's model 94 Winchester, all steel, checkered steel butt plate, old enough to say "caliber Winchester 30 WCF" on the barrel rather than 30-30. I wipe that rifle with an oily rag, give the stock a little linseed oil once a year, and call it done. As the gunsmith told me, the patina and remains of the original "browning" on the barrel and frame of that old saddle carbine were what would have made it more valuable. The attempt to "pretty up" or "restore" that saddle carbine made a mess of a classic old rifle. Some things are best left as they are if they have aged gracefully and developed a certain patina. Your vise is one such example.
