Well, the manual says "household oil", so...use that.
This typically means "3-in-1" oil, available most anywhere. It's a brand, and there are others. I think that you can get it a grocery stores! (In fact, I need some.)
I pretty much use 3-in-1 for all oiling; I use Labelle white grease for greasing. I seem to
recall Scott Mann at 3rd Rail recommending automotive axle grease for gearboxes.
Good idea. Easy to get - and very manly! - and a small can will last you a lifetime. Most lubricants will do the job; I've never experimented with oddball stuff, however you define that.
And get a tube of powdered graphite lubricant (it's dry) for such things as knuckle coupler mechanisms.