After saving as tif, engine creates dds files itself automatically, that's okay.
But, in materials, which file we should choose? Is there any problem with choosing the dds files?

You keep the original TIFF files in your development build for backup, since those are your raw files. DDS files is what your game should ship with, since they are compressed and take up much smaller sizes.

I know, I already have been doing what you mentioned.
However, the question is, should I choose the tif files in material slots, even though they will be removed after development process?

i always put the DDS file in the slots.

Thanks!

You can put either. The engine will only use the dds, essentially replacing the .tif extension with .dds. In this regard, they are synonymous.