Make sure you do this with an instructor. Being upside down in the boat can be disorientating. The pool offers a safe environment in which you can perfect all your safety and rescue maneuvers. Know these well before you need to use them in the open water. Usually the pool lessons are taught in whitewater boats.
Sea kayaks are just too big to get into most pools.
It can be an advantage to use whitewater boats. You'll also get a better feel for how to maneuver kayaks. Once you're committed you'll want your own boat. Don't buy a beginner boat if you're goal is to do long day trips and over night trips. You'll grow out of a beginner kayak almost immediately.