Lighting design for kitchen 10' x 11'
I think there are a few things to consider. 

The Ceiling Height Rule Of Thumb.

To determine how far apart to space your recessed lights, divide the height of the ceiling by two. If a room has an 8 foot ceiling, you should space your recessed lights approximately 4 feet apart. 

If the ceiling is 10 feet, you'll want the lights approximately 5 feet apart.

That being said, what one person considers too bright others do not consider bright enough. 

The thing with recessed lighting is, it is more or less, a spotlight, which can be good or bad based on preference and if you intend to highlight focal points.

What I have seen: It is common for people to regret spacing lights too far apart and/or not getting larger lights

Larger Lighting Canisters:

Pros 


In CA there are more hot days than cold days, and the canisters do
heat up, so larger canisters do better with withstanding the heat.
Extra 2' width means the lighting spreads out more.


Cons:


More power consumption (your dimmer can cross cancel this)



  Do you think the 6" lights as general lighting is enough?


Its close enough at 8' high ceilings and better if it's 10' ceilings.


  How much wattage should I get for the 6" and the 4" cans?


That's dependent on the maximum wattage allowed for the lighting canisters and what you like.

Colors in flooring and countertops, and cabinetry make a huge difference in terms of reflecting light or absorbing light.

I made a few examples for you to see. With some variations for you to see how colors effect lighting. 

Note: Keep in mind, that with recessed lighting, you have almost no lighting on the ceiling itself.