Great project, nothing like a real task to accelerate the learning ambitions and progress, and the Arduino platform with it's huge variety of compatible peripherals, libaries/drivers and community support for both the hardware side and coding, can get prototypes and proof of concept ideas up and running quite quickly.
The previous background will lead in well too, it's not always about what one knows or doesn't know specifically, it's how one goes about the task, especially debugging/developing, and there is plenty of help online too.
How much range do you need, and how many office/building walls would a signal have to go through? Low power RF has been mentioned already, and garage door opener type modules are quite reliable and available. Could be used with or without an Arduino.
A suitable direct RF alarm would give an instant response in addition to gsm, if it the had range. However, too many walls and range can limit the low power RF units, but there are also higher power, longer range rf modules available.
Gsm certainly has it's merits and one project always leads to another, so other possibilities open up, even if not pursued for this project
I've found this site https://randomnerdtutoriars.com/ really useful, and it has alot of examples/tutorials that cover areas of interest for your project. Including gsm, rf data, wifi, various sensors and modules (including tilt and motion), camera modules, cloud data etc etc
Bits and pieces can be found on Trade me, Aliexpress, Amazon etc, and even Jaycar for local shopping (but some items hellishly expensive), in addition to electronics and tech outlets.
Only one thing to watch out for, the Arduino/ESP8266 world is a real rabbitt hole...!