Some users have reported that there is no option to start the Campaign when running Homeworld 1 Remastered, or Homeworld 2 Remastered. This is most likely due to not all content having been downloaded. To remedy this, right click on the Homeworld Remastered Collection in your Steam library, and then go to "View Downloadable Content". In the window that appears, make sure all the boxes are checked (including the "Homeworld Remastered w/ BONUS Homeworld Classic" and "Homeworld 2 Remastered w/ BONUS Homeworld 2 Classic"), then allow the game to update. Once the game has finished updating, launch the game and you should now have access to the campaigns.
If you continue to experience issues with this after following the instructions above, please submit a support ticket at support.gearboxsoftware.com.