Welcome to the forum! Oil is a touchy subject, so please do your own research, and make up your own mind, before following any "oil advice" given on any forum...
There are MC-specific oils which you might consider (typically rated SF, or thereabouts, to match what was made at that time), which tend to be higher priced. Or, you could try a modern rated oil, SN, but be sure to use something which is
not energy-star rated: energy-star rated oils contain "friction modifiers" which can interfere with the clutch, ruining the plates. They're designed to improve gas mileage by making the oil 'slipperier', by around 3% -- it adds up when every car in the USA is using it, but it doesn't add up much for the individual driver.
You might try something like
Shell Rotella T (around $12/gallon at Wal-Mart; non-synthetic; no friction modifiers; diesel, but rated SN for cars; JASO rated for use in MC's; 10W-40 -- check your owner's manual for oil weight, but this will likely work just fine). If you want to live life on the edge, you could try
Shell Rotalla T6 Synthetic (around $21/gallon at Wal-Mart; synthetic; no friction modifiers; diesel, but rated SN for cars; JASO rated for use in MC's;
5W-40 -- check your owner's manual for oil weight, but this will likely work just fine; this stuff will turn over easier, at start-up, because of the 5W cold, but it will thicken up to 40 weight, when it heats up). Search the Internet for reviews on using these in MC's, for piece of mind.
Conventional oils break down at 250+ F, synthetics break down at 400+ F. Your SOHC engines likely run well below 250 F, unless you race them, so conventional oil will work just fine. The newer, DOHC engines run much hotter, so synthetic makes more sense to run in them.
If you have not
SeaFoam'ed your engines yet, consider it. By adding the correct amount to the crankcase, and running it long enough to warm the oil up to operating temperatures, shifting through all five gears, you will dissolve varnish, carbon, and other deposits, within both the engine, and the transmission, without damaging anything. Then change both the oil, and the filter, as soon as the oil turns black (almost a certainty, after five minutes of riding), as this indicates your oil and filter are full of dissolved deposits which should be removed ASAP. You won't need to repeat this process ever, if you use modern, high detergent motor oils, with routine oil change intervals. It also works great in the fuel tank: absorbs water; dissolves varnish throughout the fuel system; stabilizes gasoline for up to 12 months. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII