New to Asterisk, not sure what I need

Hello, I’ve been asked to get quotes and information together to switch our company to Asterisk. I’m not sure what I need or really where to start. I’m a programmer and IT administrator but I have very little knowledge of phone systems.

Here is a rundown of our company:

-we have 3 offices in different cities, our head office has approximately 20 people and the other two have approximately 7 each.
-we are currently on 3 different phone systems from local providers.
-all of our office are located in northwestern Ontario Canada (Thunder Bay, Sioux Lookout, and Timmins), so the infrastructure here isn’t great or cheap.
-we’ll be starting from scratch with nothing of our own.

I’m just not even sure where to begin. A lot of the terminology is very foreign to me.

Start here: