Except that your kitchen is larger than mine, my layout is a similar shape, including a big fluorescent monster in the middle of the ceiling.
Like you, I had no clue how to get the right amount of light, and I ended up even more confused after reading forum messages full of conflicting opinions, 4" vs 5" vs 6" cans, 2700K vs 3000K, this lumen number vs that number, this make of can light vs that make, formulas based on sq ft, etc.
So I went to Lowe's and looked at the can light display and noticed that the UtiliTech Pro LED Recessed Retrofit Downlight (#0113539) was the brightest (6", 800 lumen, 2700K), plus I liked the "ribbed" trim ring and the fact that the trim and bulb are a single unit. The electrician installed them last week and I could not be happier.
HD carries can lights and Lowe's has other models with different lumens and K ratings that you might like better, but I wanted an economical light that provided a bright, well-lit kitchen, and these were just what I was looking for.
There are probably going to be UtiliTech Haters responding to this message, but my rebuttal is that 1) they are a simple one-piece installation, 2) only cost $29.00 each, 3) have a 50,000 hour average life, and 4) if I'm not happy with them or they fail for some reason, at least I got to enjoy a nice bright kitchen for a while without spending much money.
One possibility for your kitchen would be 6" cans, two on the left side, one in the middle where the fluorescent is, and two on the right side. Start out with 800 lumen, 2700K and if that doesn't work for you, just try other combinations until you're happy with the result.
I just started re-doing my kitchen and as you can see in the photo, just three cans provide more than enough light in that small space. Lighting on the right side will consist of two hanging fixtures, one over the sink and one over a small island that will go where that grey table is.
P.S. I don't work for Lowe's or UtiliTech.

Here's some kitchen lighting info that might help:
http://ths.gardenweb.com/forums/load/lighting/msg010127153310.html

This post was edited by Route66Services on Wed, Jul 16, 14 at 9:43