You need 2.2l of oil, you'll need 1l/1q containers. It should meet any of these specs: API SG, SH, SJ, SL or SM with JASO MA, MA1 or MA2. A simpler solution is to buy oil marked for 4-stroke motorcycles, or the Rotella brand - just don't use conventional car oil as it has stuff that messes with clutches. It can be synthetic, semi-synthetic or conventional. The winter viscosity should be 0W to 10W, the summer 40 or 50. Most common is 10W40. You can debate synthetic with others -- synthetic it's not a factory requirement for a Ninja 300.
The OE filter is a Hiflow 303 (or Kawi PN 16097-0008). There are lots of alternatives, find them here:
Oil filter cross reference
The crush washer is 12mmx22mm. I changed the oil a dozen times on my Ninja, used the same original crush washer every time. Your mileage may vary.
All this stuff is available at Canadian Tire or any motorcycle shop, you should be around $10 bucks for a filter and $10-20/l for oil (depending on your taste). Add another $2 for a crush washer if you wish.