Basically each major location throughout the districts of New York City has a Situations Board, even your Base of Operations. This is where you will activate the Side Missions and Encounters for that specific district. Story Missions are available right from the get go and will already be highlighted on your map
When you choose a Story/Side Mission, information about that event will be displayed. This includes the mission's name, distance, if you can Fast Travel to it (instantly going to the marked location. Eh, after loading), recommended level, description, reward listing, etc.
You can do any of the Story Missions on Normal or Hard. You get more and/or better rewards if doing a Story Mission on Hard, but the NPCs also scale up based on agent levels and numbers. For example, if you have both a Level 20 agent and a Level 30 agent running a Story Mission on Hard Mode, mobs will be level 30, making it more difficult for the lower level agent.
You can replay Story Missions as often as you'd like. One nice thing about The Division is that the Story Missions (and most Open World events/locations) offer Matchmaking, so even if you don't happen to have friends around, you can still find other people to play with
Story Missions are also the focus of The Division's Daily Challenges system. Within every twenty-four hour period, three random missions are selected for Daily Challenges, which involves completing the chosen missions on either Hard and/or Challenging Mode as seen below.
Hard Mode functions just as it would if you were to replay it normally on that difficulty (explained above), but Challenging Mode scales the enemies even higher and automatically sets as though it's being engaged by four Level 30 agents, regardless of what levels and how many agents actually enter.
You will also notice the additional information regarding what the Daily Challenge Rewards are for specifically beating any of them. I believe you can only obtain the rewards for Hard Dailies once, but Challenging Dailies offer a continued reward after the fact (unless this has changed after the Incursions Update 1.1, I haven't done a Challenging Daily since its implementation).
On the track to Level 30, the best route is focusing on Story Missions and then eventually Side Missions and Encounters. The later districts offer some really good XP for completing these various objectives!
I still maintain that hitting max level isn't all that hard, but doing these missions and tasks with friends makes it all the better!
Have you completed all of the Story Missions in The Division yet? If so, which was your favorite? Do you complete your Daily Challenges? Have you completed the Challenging Mode on some of the Daily Story Missions? What would you like to see implemented to the game's mission system, if anything?