Do we want output resistance of a transistor to be high or low
Transistors are used for different purposes, and wired in different configurations to suit those purposes.

As a switch, clabacchio is(was?) correct, we usually want 0 resistance when on, infinite when off.

As a constant current source, (e.g. to drive an LED or charge a NiCd battery) we want infinite dynamic resistance, so the current remains the same as the battery voltage changes.

As a high gain amplifier, we want the output impedance (in parallel with the load impedance) to be as high as possible, so that as the output current varies, we maximise the output voltage variation, i.e. we maximise the gain. This is usually a common-emitter (sometimes common-base) configuration.

As a power output stage, we want the output impedance to be 0 so the output voltage is independent of the load resistance. This is usually accomplished by a common collector aka emitter follower configuration.

This is why high gain amplifiers that must supply high power need several stages, wired in different configurations.