If you want to be able to monitor your system you will need it to connect to your Wi-Fi.
Depending on your system. I have a system that is not tied to the internet. In my previous house the system only needed to be tied to the internet inorder for the company to see how the system was working. Buy one that allows the company to come out and fix the system with out having any internet connection.
Any kind works as long as you have Wi-Fi.
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