We have a small engineering team and the need to handle 24x7 emergency support (i.e., responding to outages in our service APIs, so more of a NOC responsibility than customer support). Today our engineers have an on-call phone, but too often we miss initial reports because the phone isn't loud enough, isn't in the right room, etc. I'm not confident we can flush out all the issues that would ensure a single person with a single phone will always answer.
We assume it would be best to hire a company as first line of defense outside of working hours to field calls and escalate internally as needed.
Basic searches for outsource NOC/customer support yields dozens of companies that look more or less identical. Any recommendations for an approach or a specific organization that offers these services? Of course we're trying to put this together as inexpensively as possible.