Making color adjustments to camera raw files (assuming here) the best way to do this is in a specific order.
Grey cards and color profiles are of limited value. Profiling the camera is a start, but understand that the profile is most accurate for the chart colors and loses its accuracy for other scenes and or products with different spectral reflectances. So a camera profile is a start but is not going to solve all color issues.
1.) Calibrate your monitor in a controlled dim neutral white light environment. The monitor should be adjusted so the white point is visually white (match a proofing or printing paper)
2) Use a white background behind your image so that when adjusting the white balance you can see if the adjusted image is slightly off as compared to that white area. Then adjust the white balance of the image first.
3). Adjust overall brightness and contrast to match the scene. The camera profile will adjust some of this but correct what the profile can not due to the dynamic range of the scene vs the much smaller range of the chart.
4.) Then adjust color mixing to fine-tune the colors that still require adjustment.
5.) Sharpen as needed for the output process.
Follow those steps and you will get a long way towards your goal