Hi, the menu is a bit specific and may be confusing, so i'll try to explain.
When you open the offline co-op menu you'll see a list of different game modes, if you want to play a campaign enter the campaign sub menu and you'll see the different campaigns you can play (L4D1 & L4D2)
If you want to play every campaign in chronological order from L4D1 first comes No Mercy, then Crash Course, Death Toll, Dead Air, Blood Harvest, The Sacrifice and finally The Last Stand.
Then comes the L4D2 campaigns, starting from Dead Center, then The Passing, Dark Carnival, Swamp Fever, Hard Rain and finally The Parish. Any of these campaigns will give you about 40 minutes of gameplay, sometimes more.
After you select a campaign you'll be presented with the stages of the selected campaign, you'll probably want to start with the first stage from up to down.
Finally you'll be able to select the difficulty of the campaign, i recommend Normal if you are a bit experienced in FPS and want a chill gameplay, the Easy difficulty is also fun if you want to try that first.
After selecting a difficulty you'll start your game in split screen and will play normally if you followed the instructions i the mod's description, if you have any doubts or trouble you can comment here or maybe start a thread in the discussion section. Good luck & have fun!