Hi,
You project is very nice and i would like to work with you in this project.
We can use any GSM module as per your budget and to detect a motion we can use PIR or microwave sensor. To make it more secure we can use cheap IR sensors on Door or windows.
To perform this task we need one microcontroller and it can be anything from 8051, PIC, Arduino, STM32 etc.,
Do let me know if you have any queries/questions.
Let us at least get into the interview stage and discuss things.
Hoping to hear from you,
Jaydip Kathiriya