The five-minute watchlist
Start with what the router reports about itself: CPU load, memory use, uptime, interface state, and storage. Uptime is the most human of them — a router that rebooted last night tells you more than a slow trend line, because a reboot is an event with a time and, usually, a cause.
Interface state catches the failures that subscribers feel first: a port that is up but flapping, traffic on an interface that should be idle, or one interface carrying far more than it should. These are visible long before anyone files a ticket.