domoticz LOL or similar. just using various zwave devices and stuff.
Getting something like that monitored would be difficult. Alarm companies want to minimize false alarms, they aren't prone to trusting their customer's ability to write their own alarm logic.
Many areas have alarm ordinances requiring a permit in order for the police to even respond to a call from the monitoring company. The permits often impose requirements about how the alarm functions to reduce false alarms (look up CP-01). Monitoring companies also like the ability to remotely adjust things if needed.
The only practical way to professionally monitor a homebrew alarm is by making it provide simple outputs that indicate the alarm state like a relay that closes when the burglar alarm is going off. This would then have to be hooked either to a real alarm system or a communicator that supports simple inputs like this (a few do, but this provides no info about what zone triggered the alarm). You'd pay close to $20/mo in monitoring and when your system generates a false alarm you'd find yourself in hot water.
The ring system would be a far cheaper and more practical option for you.