Other quests require certain weapons or outfits.

With that difficulty increase, the loot will also get better. You'll start receiving multi-part quests which get increasingly difficult. As your vault gets bigger and gains more dwellers, the quests will start getting harder. Charisma may help with speech checks that pop up on certain missions, but I cannot confirm that.

Higher endurance = less stimpaks needing to be used. If you notice your dweller getting hit 2 or 3 times before firing back it's because their agility is low. Agility determines how often your character will shoot. Certain special stats will really help you out on quests. (My A team are all level 50 with maxed out special stats.) You can again abuse the system clock to speed up their training times. Your job with them will be to send them out in the wasteland to level up and get their special stats as high as possible in the training rooms. While doing that, pick out 9 dwellers who you'd like to be your A, B, and C teams. The quests you get at the start of the game should be quite easy. Faster you get 3 questing teams out, faster you get this finished. Anyway, there's no one solution because every quest is a tad different, but here are some tips to make your questing quicker and smoother: Obviously first you're going to need an overseer's office. However, when moving time back without quitting, the game's audio will cut out. You do NOT need to reload if you're moving time forward. (Settings > System > Time) Once you reach the +14 time zone, quit the game, turn it back to -12 and reload the game. This is going to take some time, but can be shortened immensely by changing your system clock.

Fallout shelter best pet for questing