Yeah, Can o' worms has been opened!
Here's my two cents;
1) Use a motorcycle-specific oil, or AT LEAST one that has the JASO-MA rating. Though, preferably, a motorcycle specific oil! They won't harm the wet clutch like some car oils will, and they will have additives formulated for the shared transmission oil, wet clutch, etc.
2) Use the weight the manufacturer recommends. Don't try to play chemist. Lots of people will tell you some blanket rules like "Always use XW-XX in certain temps" but every bike is different. Being an overhead cam engine, heavier weight oils can cause issues. Stick with 10W-40, which is what Kawasaki recommends for the 900. Stay away from oil additives and intentionally mixing oils (half this, half that). I'm not sure why people do that, but the oils have been formulated to work in a particular way by some well payed engineers. Adding stuff or mixing oils is not a great idea. Note that having a little oil left in the engine when you refill it with fresh oil is not 'mixing oils'. But I've seen a few folks who will use maybe 2 quarts of one brand and weight and a quart and a half of another brand and weight, intentionally, because they think it's better than using just one. Don't be tempted to play chemist. If you want to do that stuff, get a degree and start working for the engine oil companies!
3) Oil change intervals are more important than oil brands, IMHO. I would not exceed Kawasaki's recommended 7,500 miles, though you'd probably be better off to do it much sooner. Note that synthetic oil does not automatically allow you to go longer on oil changes. SOME synthetics are rated for extended drain intervals, but not most. Most synthetic oils are intended to be changed at the same intervals the conventional oils are. However they do offer better protection and better resistance to certain things.
As for me? I run either Valvoline Motorcycle Synthetic 10W-40, or Amsoil. About to switch to Amsoil as I can get it from our forum Amsoil dealer for about the same price as running the Valvoline (Amsoil Dealer Group is his name on here if you want to send him a PM). I change it every 5,000 miles. In theory I also wouldn't go more than 12 months without an oil change; but at 15-20k miles a year, that's not gonna happen anyway.
To dispell a couple common synthetic rumors;
1) You can mix, match, and switch between synthetic and conventional all day long. They are 100% compatible. Certain fluids are not compatible, so people assume ALL fluids are not compatible. Not true for engine oil. So if you're considering switching to synthetic; no- there's nothing you need to do. Just change the oil.
2) Yes, you can run synthetic in your 900. It's just oil. It has some advantages, but it's still oil.
Anything you choose will likely do just fine for the life of the bike. Lots of guys have 100k+ on inexpensive, motorcycle specific, conventional oils changed at reasonable intervals (before the 7,500 mile interval Kawasaki recommends).