Marque LED chaser

LED forward voltage (Vf) and nominal operating current?

It sounds like your first requirement is that only one LED is on at a time. Is this correct? If so, this is a common circuit using two CD4017 CMOS counters. The counter output can supply only around 4 mA, so you might need external drivers for your desired brightness.

With different LED connections, the same circuit can have all LEDs on except the one that is traveling. Having one circuit that can be switched between the two modes is another layer of complexity.

ak