People wonder why the engines on the old cars lasted so long considering the abuse some of them had. The oil bath air cleaner was the most efficient ever made. It was discontinued due to the fact that it protected the engine so well. I've taken apart engines in jeeps to reseal them and found almost none of the wear on the valve I find in newer engines operating in a dusty environment. The oil is a dead stop to all dust, dirt, chips, and all other particulate matter. Take an old oil bath apart that has been used for a while and you'll find it has a pretty good layer of sludge down in the bottom. That sludge is all the crap that the oil stopped from getting into the engine. That is why they oil foam air filters. The oil will grab most of the smaller dust particles that can normally get through the filter.
Sorry, but oil bath air cleaners are very sub standard compared to virtually any paper style element.
Oil baths work by impaction, whereby the contaminant hits the media (usually metal shavings) and falls into the oil bath which holds it.
Lots of contaminants flow past the media (lest face it, the gaps are huge) and into the engine.
Can't remember what efficiency they have, but it's pretty low.
A friend of mine who is a filtration research engineer (he has a PhD, has written peer reviewed papers and worked with the biggest filter media manufacturers in the world on R&D, including Cummins Filtration (Fleetgaurd), Mann-Hummel in Germany and Donaldson) has a pretty low opinion of them, and one of his old Land Rovers had one. He ditched it for a Donaldson.
Generally with oil baths you used to use the same oil that went into the engine, eg. my old Tractor specced 20W-40 oil in both engine and air cleaner, so I just use a 15W-40 these days.
I'm sure a 10W-30 would be fine, it's only there to hold the dust that's dropped into the sump.