+1 for Scotchbrite nylon scourers. The different colours signify different grades. I think that the dark green used in the kitchen are the hardest. They will remove rust, but unlikely to remove much metal, look how the material wears out with use in the kit chen on ceramics. We used to use them in industry for cleaning dirty or rusted surfaces. Would advise using oil rather than paraffine (kerosene), it can absorb water, so that you would plant the seeds of more rust.
For iron or steels to rust there must be water and oxygen present. You won't keep out the oxygen, unless you vacuum pack the lathe, so once clean, seal out the water with oil.
In my previous shop, when cold, the oil on the bedways of my Myford would turn milky as it emulsified with the moisture, so had be wiped off and replaced after use. Keep the atmosphere as dry, as possible, and above the dew point, (I switch on a 240 volt, 60watt tubular heater when the weather is cold, in a well insulated shop, in UK, and VERY rarely see any rust). If you are in a high humidity location, the problem is greater, and you may even need to use a dehumidifier.
Do not heat the shop with any combustion heater, (Woodburner, gas fire, liquid fuel heater) since these all produce moisture in operation; and Carbon Monoxide which will not do you any good.
If you want to ventilate, have the vents at floor level. Moist air is heavier than dry.
Howard
Edited By Howard Lewis on 14/02/2016 23:45:53