I have added a new external drive (G) and want to move all my photos there. The situation is anyhow such as I have imported my photos on C only partially to LR . So I am pondering here should I first import all photos to LR and then from LR move them from C into G or move all photos from C to G and import all to LR?
If the number of files to be moved is large, you are probably better off moving them using the OS tools then relinking them in LR.
As long as the directory tree on the old disk matches the layout on the new disk, in LR you will need to relink only the top directory in the folders panel and the rest will happen for free.
My recommendation is to move the files outside of LR, relink the top folder in LR, then import the rest of the files.