Getting a backpack in FO76 is actually not that easy. It can potentially take a lot of time depending on how lucky (or unlucky) you are. For example, I did the quests that are required (more on that below) but at the last stage the game was literally refusing to let me find the mobs I needed and I lost many hours stubbornly trying to find them at all kinds of locations with no success.
I gave up and went with the small one which is super easy to get.
Normal vs Small Backpack
The only difference between these (apart from how hard the first one can be to get) is their carry weight bonus. Small backpack adds half of what the normal one does. Both scale at leveling up and both can be modded.
So if you don’t really care that much about something you might not even wear all the time, just go with the small one and get the plan right away at Morgantown Airport Terminal.
Watch the video for the exact path you need to take. Be prepared to fight off a lot of scorched on the way.
To embark on a quest chain to get a normal one, you will need to join the pioneer scouts at Pioneer Scout Camp in Toxic Valley.