Brilliant!
Thanks a lot guys for the quick replies; getting there already ... really helpful.
It's my mistake but I forget to mention that I intend this to work autonomously. This means that basically it should connect wirelessly to a local wireless router (the password will be configured by the end user on the setup phase - software - I think this is the best approach but if you have other ideas that you could suggest you are most welcome to do so - you are the expert 
). Afterwards the board should connect (let's say every 5 hours) to the router and request data via an API. Depending on the API response it should light up an LED (or not).
So based on this approach I think I can say that the connection between the Arduino Mini and wireless router should be made via WiFi (so we can drop the bluetooth or IR components in this case). If this is the case, which WiFi components/shield would you use? If you could drop me a link even better.
Also, I've managed to create already (using my Arduino Uno board) a connection between the board and PC. I've also created a really simple user interface in Visual Basic just to test this. Right now I have a small application on my PC trough which I can turn ON/OFF the LEDs from my board. Maybe it's not related but had to try this so I can taste the software part and how things work.
Again, it's a barebone idea, I try not to complicate it way too much so I can learn while doing this