Congratulations on your new 250R. I have your Ninja's big brother, the 14R. Kawasaki dot com has a excellent resource for vehicle part numbers and a on-line shop like Ron Ayers (located in Greenville, NC) is a excellent source for OEM parts such as your oil filters, drain plug gaskets, air filters, etc.
Stick with a motorcycle specific oil. Valvoline (and Castrol for that matter) motorcycle oils are routinely on sale at most autoparts stores for $2.99 a quart throughout the summer. Get a few bottles to last your riding season and be done.
Stick to OEM filters and mail-order them along with your drain plug gaskets in quantities to last the season. It really isn't any more expensive to keep the bike OEM.
drain plug gasket: 11061-0417 is $1.19
oil filter cartridge: 16099-003 is $7.02
Add a couple of quarts of motorcycle specific oil and you're in under $20 for a season of riding.
Just a FYI, I spoke to Valvoline about the difference between their motorcycle oil and their ATV oil (all mineral oil, not the synthetic product). The motorcycle oil actually carries that JASO MA2 rating while the ATV oil carries the MA1. There's more friction afforded to the clutch with the motorcycle oil vice the ATV oil.
That's my $.02.. enjoy your new toy!!