Mobile DTE Oil, Heavy-Medium, Circulating Oil, ISO 68 is what I have actually used for the past decade or so. Last time that I bought it was from Enco for about $22 US per gallon. Enco no longer exists and I'm sure the cost today will be higher.. Tractor Supply had SAE 20 ND for a while but I understand that they have discontinued it. But the Mobile DTE works as well. And should always be available from someone.
I forgot to comment on the spindle bearings. One thing that you DO NOT want to do is to put grease on them during assembly. What will eventually happen is that the grease will harden. Over time and depending upon where it got slung during the first few minutes of operation, grease could block the oil from getting to the rollers. There is no way to tell that without pulling the spindle. So don't put grease on the spindle bearings.
At this point, someone sometimes mentions that automotive wheel bearings are tapered roller and use grease. But wheel bearings are easy to service compared to spindle bearings. Plus they are run looser than spindle bearings. And finally, the reason that they run grease instead of oil is that with oil, they soon leak. Which is an issue on vehicles but not on lathes.