Here's how it would normally be done:
+ Convert RAW/MLV clips to CinemaDNG with RAWMagic
+ Convert GoPro footage to ProRes with 5DtoRGB or edit it natively in Premiere
+ Import footage into Premiere Pro
+ Edit DNG/ProRes/MP4 natively in Premiere
+ After edit is locked, export OMF of sound for sound mixer
+ Export XML of edit sequence to Resolve for color correction
+ Color correct in Resolve while sound is being mixed
+ Render color corrected media, export new XML from Resolve, import back into Premiere (the term for this is "roundtrip")
+ Back in Premiere, marry completed sound mix to picture, add titles, credits, etc.
+ Export master from Premiere to ProRes MOV, DPX, etc.
+ Create deliverables from master, from H.264 versions for the web all way up to a DCP.
Don't color correct before you edit. You need to color correct after editing so you can make all your shots match.
Which color grading program should I learn?
Resolve. Don't waste time thinking about this. Just go download it now and start learning it.