liteManiac, I know you narrowed your choice for your first LED flashlight to the Fenix LP1 and Peak Caribbean, and asked only about those two lights. Like BentHeadTx, I have the Peak Mediterranean and Fenix LP1. I agree with eveything BentHeadTx said, which I think was a very good analysis of the two lights. As between the Peak and Fenix, I would go for the Peak if the cost difference is not an obstacle, and you are okay with using CR123 batteries. As a CPF member, you can buy CR123 batteries from Battery Station for 1.00 each.
I cannot resist, however, suggesting that you consider the Jil CR2 1.3 (up) or Jil Intelli for your first LED flashlight. They are roughly in the same price range as the Peak. I think that if I were to do it over again, and had the Jil Intelli been available, I would choose the Jil Intelli for my first LED flashlight. CPFer goldserve (apparently a flashlight genius, along with several other CPF members) created a modification to the Jil DD (direct drive) that you can buy from Warren aka liteMania by going to the Dealers Corner of CPF. If the Jil Intelli seems too complicated, then consider the Jil CR2 1.3(up).
Both the Fenix and Peak are good choices, however. Good luck on buying your first led flashlight, but be careful. It may not be your last.