I did some research to do our kitchen, and here is what I came up with. Its now installed and works very well.

Recessed lighting:

Use 4" for task areas only - these are expensive and the trim options are limited

Use 5" for general lighting if the room is smaller in size or has less than 9 ft ceilings.

Use 6" for larger rooms with higher ceilings
The size of the can does not indicated how much light you will get - the wattage of the bulb does.

In general, you need between 2.5 to 3 watts of light per square foot.

I have more details on my blog.

Here is a link that might be useful: 10k Kitchen Remodel - Lighting

Spacing generally hinges on the type and wattage of bulbs you use, the amount of light you need, and on the height of the ceiling. A common rule of thumb is to place cans 4 feet apart, but that rule assumes 6" cans and very inefficient R-type reflector bulbs; if you're using smaller cans or other bulb types, that rule doesn't do you much good. What sort of room are you planning to light?