What kind of oil do you guys use?

Chain saw bar oil and Lucas oil additive mixed 50/50

Is that this stuff?

Lucas 10063 Engine Break In Oil Additive with Zinc

-Shay

No. I use the oil stabilizer. Comes in a white bottle. It's thick and sticky like honey. I find it helps stop oil splatter on your timber and is an excellent lube.

So this stuff then.

Lucas Oil Stabalizer

-Shay

Yep

Ba!
cheapest possible 10W30.

So do you just have a little squeeze oil can and apply it to the chain and run it a little?

I have a little red plastic oil can, I oil the chain after every mortise or so... I think it's better to put oil on the chain and not run the machine so the oil has a moment to run into the chain, rather than get thrown off.
10W30 also works fine for steering fluid in my tractor, bar oil for my chainsaw, and engine oil for everything but my tractor.
Heck, it even makes a decent sandwich spread, add a little mustard, maybe some pickles...