mrfsx2015

I see a problem right off the bat.  You shouldn't have to select Story mode bro.  That is regular GTA.  Your RPH is not installed properly.  The newer ones go straight to Story mode, as the devs know that is the only way you can play is Single Player.
EDIT:  Sorry I did not read your full problem.  Ya the first part where you mention that you see the Story Mode menu, that is just plain GTA that is being loaded.  So your Rage Hook is not installed properly.  It could be a pathway issue as well.  Make sure the game is installed in the correct pathway.  Steam users have a very distinct pathway we must follow.  So if you put this stuff on another drive it can become a pain.  You can still do it though. You just have to stay consistent with everything from the Steam or Retail install pathway, LSPDFR 0.3 needs to be able to find your Grand Theft Auto V game directory as well. I found the Auto installer to work well.