It depends on what you are looking for.
Most people calibrate the meter only, the sticker on the meter makes it look like you are using a calibrated instrument. But unless you account for the accuracy of the probe you really know nothing about your measurement accuracy. For instance, a type K probe can add up to ± 2.2°C error to your measurements. This measurement can be accurate enough in a lot of cases.
If you want or need more accuracy in your measurements the optimal method is to calibrate them as a system and keep them as a system. But most users want to be able to use multiple probes on each meter, so this doesn't really work.
If you have multiple probes my suggestion would be to calibrate the meter and probes separately, and apply the offsets for the probe that you are using.