On a Ninja 250, it is recommended to wait until 5,000 km before you switch away from the regular "dino" oil, or mineral oil. Kahuna sells this, and it's Kawasaki's M4 oil. I used this until 7.5k. However, this recommendation is purely based on hearsay, and I doubt you'll find any official material indicating this. So really, it's arbitrary.
Now, if you want to use synthetic, there is no reason not to use Shell Rotella T6. I've been using it in my 250 for almost 20k, and it works wonderfully. I change oil and filter every 5k, and the oil doesn't look too dirty. This last oil change, I've pushed it to 7k, so we'll see what happens!
I also use the K&N 401 filter. You're right, there are other brands that are exactly the same. Good filter, and it looks pretty clean when I change it. I could likely change the filter every other oil change, but for $8, why not?
I bought my oil from Walmart in the US. I stocked up at $20/gallon. I bought the filters from Bob Weaver's in Niagara Falls, NY for $8 a piece. I also stocked up on these.
Use the Amsoil if you want, but personally, I think you're spending more money than you need to. I would run better quality oil in a track/race bike, not a street bike.