I think that before start writing code, it is most important to first connect your modem with a terminal software and drive it through there. You will see a lot of things that are not directly visible through code debugging. You will save a lot of development time in this way.
Start with the basics. Make and receive calls and sms, delete sms, calls listing and in general all basics that you already know from your mobile phone. Then you can write an MCU project faster.
When you will be needing more commands, you can first test them in the terminal software and then write the MCU code for them. I think this is the optimum way.
By the way, I believe that Windows Hyperterminal is an awful software. You can check out some more terminal software through this thread:
https://www.edaboard.com/threads/228501/
Hope that helped,
Alexandros