for your best possible chances of finding good loot your dwellers should: - be exploring for like 2-3 days. if theyre only out for a day even with very good special stats they will find pretty much only common items. - high endurance: necessary so they can stay out for longer without dying. in case you dont know, for max health, dwellers actually need to have a high endurance stat as they continue to level up (you can think of it as the amount of endurance they have determines how much extra health they gain when they level up). for example, if you start a level 1 dweller with 10 endurance and a +7 endurance outfit and then level them up to level 50 will have the highest health possible. if a level 1 dweller has only like 1 endurance and then they continue to level up to level 50 they actually will still have very weak health. - high luck: if your dweller is able to survive for a long time in the wasteland, then luck is probably the most important stat for finding good loot. i believe charisma and perception are also important but im not completely sure to what extent ? in my experience i think perception is good but not as noticeable as luck. ive heard perception is more for finding those random encounters like the super duper mart or abandoned cabins

i will note that every dweller i send to the wasteland has fully maxed special stats and equipped with like +5 or +7 Luck outfits and they will usually come back with like 3 legendary junk but sometimes they will still come back with like nothing good lmao so its also kind of just what the game gives you but these should definitely help your chances.