The order of processing affects the result.

When pre-processing videos for encoding, the order of the filters does have an effect on image quality and the processing time.
I always try to follow the order below for best results.

1) De-interlace if needed.
2) Frame rate conversion if smaller than original.
3) Cropping if needed.
4) Resize if reducing image size.
5) Color space conversion.
6) De-noise.
7) Resize if enlarging image.
8) Frame rate conversion if greater than original.
9) Sharpen or other enhancements as needed.

The idea is that first you start with a progressive image to then reduce the size and number of frames to work with smaller data sets. Perform color space conversions and apply any noise reduction if needed. If you are enlarging the image, do it after the color space conversion and noise reduction. Then apply frame rate conversions.
Finally perform any sharpening or other image enhancing filters to the final image.

Preprocessing

There are great benefits from processing videos prior to encoding. The right preprocessing can gain you time, bandwidth and increase the image quality of your final video.
There are six important processes that you should consider applying to your source video prior to encoding:

1) De-interlacing. Will avoid creating line crawling artifacts.

2) Noise reduction. Motion adaptive noise reduction can greatly improve the performance of your encoder as random noise in images produce artifacts in the encoded image.

3) Color Space Conversion. Use of high quality color space conversion algorithms can reduce color bands and “blotches” as bit reduction and color plane decimation (going from RGB or 4:4:4 to 4:2:0 for example.)

4) Resampling and resizing. Will greatly reduce encoding time and improve quality. Specially true if you are down sampling or reducing sizes.

5) Cropping. Same as above.

6) Frame Rate Conversion. Will allow you to use high quality frame rate conversion algorithms. If you are reducing the frame rate, you’ll have the added benefit of faster encodes.

De-interlacing algorithms

De-interlacing algorithms can be sub divided into two broad categories:

1. Spatial Based
2. Motion Based

Some popular spatial based algorithms are:

• Simply weaving the odd field and doubling each line. (Produces aliasing)
• Averaging or blending both fields. (Produces ghosting)
• Edge dependent interpolation techniques between adjacent lines in odd-even fields. (Few artifacts if edge direction is inaccurate)

Some motion based algorithms are:

• Selective blending (or motion adaptive blending) basically only blend areas where there is motion and weaving where there is none. (Few artifacts if motion calculation is correct)
• Motion and edge adaptive algorithms combine edge interpolation techniques and motion adaptive blending. (Fewer artifacts at computational expense)
• Motion compensated algorithms can use the information to find the matching blocks in the neighboring fields. (Fewer artifacts at computational expense)

Be sure to check what algorithms your encoding software implements, it might have a great impact in your final video quality.