What to Look for When Choosing a PCB Assembly Service?

When a project moves from a breadboard or prototype to a custom PCB, getting the board assembled can sometimes be more challenging than designing it.

There are quite a few things to consider when choosing a PCB assembly service — component sourcing, SMT placement, through-hole assembly, board quality, inspection, turnaround time, and of course, the overall cost.

I've recently been looking into PCB assembly services and came across PCBCool. They provide PCB manufacturing and assembly services, which seems useful when you want fabrication and component assembly handled through the same supplier.

I'm curious what other makers and electronics developers usually prioritize when choosing an assembly service.

Would be interested to hear what has worked well for others, especially for Arduino, ESP32, robotics, and other small-batch electronics projects.