Welcome to the water rocket forum!
This type of bottle is not suitable for a water rocket which consists of multiple bottles because the bottle type has patterns molded into the sides.
Also it isn't enough think walled and would explode if you pressurise it.
The idea to make three segments is good because it allows you to replace a single segment in case something goes wrong.
The connectors you searching for are called "Tornado Tubes".
I highly recommend you to use the forum search function, there are thousands of great tutorials out here which explain every detail.
This tutorial, for example, explains the construction of a two meters large water rocket, including a suitable launcher and a parachute system:
http://www.wra2.org/forum/viewtopic.php?f=46&t=2691
Also you will find some easy understandable drawings and some information about the launch preparations there.
I wish you good luck and much success!

Julian from Team Raketfued