4" the max all LED 4000K bulbs and pretty sure this was posted with anothr posters name asking how many . IMO no such thing as too bright in a kitchen I have 10 heads on 2 reacks in mine all LED 4000K I like kitchen lighting to be layered so under cabiet on one switch, pot lights on a nother and the pendants over the island on an other . That way you can tone down the light anytime. I usually just use the light over the island when I am finished cooking and I am now serving dinner.

1200 lumens at 9' height may be too bright. I would do 600 or 800 lumens. Also, 4000k color temperature is too blue/cool/stark for most people. I would go with 3500k or 3000k. Or the best would be color changing LEDs so you can try the different settings and see what you like.

The can placement shown has the cans over the aisles so you will create shadows when standing at the worktops. The lights should be centered on the counter edge- about 25” off outside walls. 4” cans. I like to get standard Edison base cans with par 30 3000k bulbs but that’s a personal choice. More is better, on dimmers. My kitchen is 12x 19 and has ten cans plus a hood with lights, two pendants, and led under cabinet tape

Thanks for the feedback everyone, this has been quite helpful. So I've revised the plan as follows:

If she places the cans as in above picture, and puts a chandelier over the dining table, will she have enough light at dining table and at island?

4" diameter 800 lumen cans with wide beam angle, spaced starting 3.5' from left wall and also from right wall, and 4' apart from each other. Also spaced 2' from back wall right over edge of base cabinets.

On dimmers in case 800 lumens is too bright.