I normally would say go for it, but since you would just be starting your skin will be extra sensitive, and at the beach, that can be harmful - considering Benzoyl Peroxide makes your skin more susceptible to sunburn, the saltwater might be a little harsh and your skin probably will be flaky.
I would wait until you get back, just so that way the regimen doesn't get in the way of you having a good time, because it can be a little hard to adjust to such a time consuming, dedicated routine when you're on vacation.
I would go out and get a nice sunscreen to take with you, and if you get oily, some oil absorbing sheets. Also, a good moisturizer just so when you get out of the ocean your skin doesn't go crazy because it feels like it's being attacked, lol.
Here's a list of sunscreens with safe ingredients: http://www.ewg.org/2...ort-sunscreens/
As for moisturizers, I recommend Cetaphil, CeraVe, Burt's Bees... Things of those nature. I wish you well on your vacation and embarkment of the regimen!