The first mission that you should take on after you are released into the world map section is not the main story mission, in the third zone marked with a blue Story label, but the first Order mission instead. This is a side mission that will earn you more AU to buy parts from the store, which in turn you can use to make your AC more powerful before taking on the next proper mission. You can find this mission in the second zone, marked with a red Order label. Hover your cursor over the mission to get a brief overview of the mission to come.
Your objective here will be simple: Destroy all of the enemies in the territory. Your enemies in this case will be former City Police, meaning that their inventory will be a bit limited. Essentially, this will be the perfect first mission, as the enemy forces consist merely of tanks and weak aerial units. You will note on the Mission Select screen that the maximum number of sortie members is two, but don’t even both hiring a mercenary to accompany you into this battle. It’s straightforward enough that you shouldn’t need much in the way of additional backup.
Begin the mission to view a brief cutscene establishing the area and your mission. When you being, you will find yourself on train tracks in the desert. Activate boost and charge down the train tracks to find the first two tanks. Dodge to the left and right while still boosting forward to avoid their shells, then take them out when you can safely activate a lock on. Keep following the tracks as they loop around to the left. You will be met with two more tanks, along with three aerial units. Dodge the shells from the tanks just like before, taking them out when you get close enough. Then bring down the aerial units. You can do this using missiles or the cannons on your shoulders, but with these weak enemies it may actually be best to use a Shotgun of some sort. The spread from a Shotgun will be enough to rip through several aerial units at once, tearing them apart like tissue paper.
Keep following the train tracks after you take out these enemies. You will be met with the final group of enemies, consisting of five aerial units and three tanks. The strategy here should be the same as before. The tanks are weak and can be taken out with a shoulder-mounted cannon as your approach them. Get the aerial units in your sight, and take out two or three at a time with your Shotgun. As these enemies fall, the mission will complete and you will receive your bonus AU.