What you mean by connecting to the router for mobile alert? you want it to be IP enabled (connecting to internet)? or simply want a system that can call your mobile phone via Landline?
If you want the latter, I believe the HSA6400 by Yale offers the best value for money (very reliable and uses industrial components). The alarm system will dial out to 3 numbers (mobile/landline) during alarm, and you can remotely disarm your system via pressing the number keys (after you enter the password).
If your house have no landline and want a system that call out via a GSM module, and if money is no objective, you can get a Menvier, Scantronic, system (their GSM module alone, cost more than the whole Yale alarm). It is very fully featured, and suitable if you are technically minded. This will allow SMS beside voice call.
If you want an IP enabled system, you got a few choice. You can go for built in HTTP server like the Visionic Powermax pro which is ip enable (self host), or you can get a third party host system like those offered by Intamac.
I personally felt IP enable system is overkill for normal household, since it offers few advantage unless you start latching on IP cameras and other high bandwidth device to the system. In addition, you have to route through your friewall etc in most cases.
All the system i mentioned above are generally reliable and differ only by feature required. Hope this helps.