I guess I would start with the Laphiog since its the best know and will give the best base to judge the other by on what a Islay should be. And then from there you can go the Lagavulin 16 and Caol 12. I would drink them in this order if it was me.
1. Laphiog 10- to set a base.
4. Bowmore- I am on of the few that prefer Darkest but to stay to the Islay, I would get 12
5. Bruichladdich- Classic to get a sense of what their base brand is and then try there heavy peated.
6. Kilchomen- 100% Islay if you could.