Easiest way to solve the checkpoint system is to use the mission section that has 20 boxes that are never used except when you create a new character or buy a trials card. Each card (VoG, Crota, PoE, etc) fills in a checkbox as you complete a section. You can group up with anyone in the game, but you can only resume where the player that is the least furthest along is at. Each card should track the different difficulty levels as well.
After TTK, there is going to be a new tab in the menu to track quests. I'm hoping our checkpoints / clears for raids, PoE, etc. are also displayed there, similar to the Advisers tab on b.net.