I would prefer in the below order
1. Resolution
Resolution represents the measurement system’s capability to detect and indicate small changes in the characteristic measured. Resolution is also known as discrimination. E.g. a tape measure with gradations in cm cannot be distinguish between measurements lesser than 1 cm, like 2mm say.
If an instrument is not able to measure the required attribute in the first place, there is no point in proceeding
2. Bias
Bias can be defined as the difference between the mean or the expected results (say of a standard) and the true/accepted reference value, and can be designated as a systematic error. Bias is checked using calibration.
Once an instrument is able to have the necessary resolution, as above, bias would be the second thing to check.
3. Linearity
The next question to answer would be if the procedure is able to delivery accurate and precise results (established above), over a range of values (higher or lower)?
Linearity answers this question and performs calibration over a range of the measurement.
4. Precision
Precision is also an important parameter necessary to demonstrate that a procedure will provide valid result, and helps in quantifying the random error. There may be a myriad of sources of variability in each measurement and many of them can be transient and cannot be easily identified or controlled. Therefore, a variety of approaches are used: Repeatability, Intermediate Precision and Reproducibility.
Once all systematics errors are noted (and removed), through Bias estimation, Precision would be the next thing to check
5. Stability
Stability, may be interpreted as the change in bias of a measurement over time and usage when such a system is used to measure a master part or standard. One can interpret a stable measurement as one which is in (the variation) is in statistical control.
Once all of the above are established, Stability can be used as an on-going check