Most small lathes and mills can do quite well with any good grade of way oil. Mobil Vactra 2 is fine. I use a Shell product that was recommended by the local distributor, seems to work fine. Same thing with gear oil. Most equipment should have documentation of the recommended lubricants, older stuff may list items that are no longer available. No problem, just take the list to your local distributor (or call MSCDIRECT if you live in the boonies) and let them help you out.
As for cutting oil, on the CNC lathe and mill, which we use almost every work day, we use a water soluble cutting fluid. We buy it in five gallon buckets and dilute it about 100:1 water
il. As we run the machines some of the water evaporates and we top it up with plain water to get it back to the proper concentration. It looks like 2% milk. We use it for all machining operations on all metals including steel, stainless, aluminum, brass and titanium.
On the manual mill and lathe we use synthetic fluids such as tapmagic, Sgt Brown's cutting fluid, and other similar lubes. These are not meant to flood the part like soluble oil, they act right at the surface so a little goes a long way. I buy 1" bristle brushes at Harbor Freight by the box. A few drops of oil on the brush and then "paint" the surface or the tap before you cut. A little can last a long time for hobbyist operations.
Cutting fluids are supposed to do three things:
1. Reduce friction when cutting. This includes preventing chips from sticking to the tool.
2. Cool the tool and part.
3. Flush away chips.
Soluble oil and flood coolant does all three. Spot/surface fluids can only do the first, so speeds, feeds, and cutting depth has to be controlled to prevent overheating tools and the work. Not a real problem for the hobbyist, mass production is another story.
Haven't used pipe cutting oil much, it's closer to gear cutting oil than anything else and is intended to be a pure oil flood coolant. I am not sure but I thought many pipe cutting fluids contain sulfur, which can react with some metals. There are better fluids available at reasonable cost.
A lot of machining operations such as turning can be done "dry", but I would NEVER recommend tapping dry, especially aluminum and stainless. In a pinch WD40, kerosene, even 3-in-1 oil is better than nothing. (Alox bullet lube for tapping?)
Most vendors and distributors know more about lube than I do, I tell them what I need and let them earn their money.
By the way, if you have a good air compressor setup using high speed air as a coolant when machining can help keep tool/part temperatures down.