Your still half way there. No worries - your on the right track.
Check this Unity answer and this answer and this video. They should help. Follow them completely, not partially.
Then when you have your texture setup correctly in c4d and exported into Unity, follow the instruction on materials and textures on this page.
Hi, do not export to obj from Cinema, obj exporter/importer doesn’t read/write materials correctly. Best format to use is fbx, just remember to set the normal angle to calculate in Unity import dialog and adjust to the models needs.