How to send info between two different phone apps and a server

High level question.

I am very new to Droid app development and I only know how to make web apps. I need to create an app system that allows a user to operate an app on one phone, after receiving data from a server, and then pressing buttons to send info to launch and control another app on another phone that I will create, and this app will send and receive data from the server and also send data back to the other phone. So we need two phones and one server that can all talk back and forth with each other

What is the best way to send data between apps so that one app can launch another app on another phone and exchange data or instructions with it? Http? UDP? Other standard? And what is the best hosting solution? We want everything to be in the cloud. So far, it looks like maybe Google App Engine might work or Windows Azure. If this is correct, which would you recommend?