Sorry to hear about your recent burglary. My primary residence recently was burglarized (likely by neighbors, as well) and it's really upsetting. We went with Frontpoint Security. It is totally cellular and connects flawlessly with our iPhones. Evidently, it has it's own cellular device in the control panel that is not connected to anything in your home for added security. You have the option to customize your package with door/window sensors, motion detectors, and cameras. You can also add on smoke/CO2 detectors. You do have to pay for the equipment upfront, but if you "pass" their credit check it's pretty cheap (ours was about $125 with the camera, 2 doors, 2 motion detectors). It is $49 a month, but only $45 a month if we didn't have a camera. Also, there is a 3-year contract, but it is transferrable across different residences so you can move the system.
So far we are satisfied. Hope this helps! Good luck! Also, don't forget to file your HO claim. If you need any advice, I just went through this process and would be happy to answer any questions.