I installed an old school alarm in my house about a year ago and went with a Texecom Premier Elite 24 (a well known brand in the UK). It has some of the features you describe such as a keyfob reader on the keypad at the door and an IP Module that you can use to program the panel with some Windows software, or use a keypad app on your phone.
Anyway, a nice feature it has is 8 'digicom programmable outputs' which can be set to notify certain states of the alarm such as whether it is armed, whether it has gone off, confirmed alarm (> 1 zone activated), and literally hundreds of other states.
So, I programmed these outputs and hooked them up via some breadboard circuitry to a $19 Particle Photon (
https://www.particle.io). This is basically an Arduino with built in WiFi and a web based IDE. It even has an API for IFTTT. Particle now make a unit called the Electron which has a built-in 2G GSM or 3G UMTS radio instead of WiFi and this would be pretty ideal for alarm monitoring. I may get one of those one day.
So far I have everything hooked up and it is working great via some demo code, but haven't got around to writing some meaningful sketches for it yet.
I knew very little about electronics, nothing at all about microcontrollers and it is all a learning curve for me. Of course I don't think your Insurance Company would be interested, and it is some time investment. But it is also quite satisfying and fun.