Oh, that locket? SNeak really is your friend there. I don't think I did that one until I was a little levelled up (but not much, I did it before the corvega quest, probably one of my first quests though really).
Maybe work on finding resources for your settlement to build first, I found that was a great way to level up (also, building new stuff gives you experience
). It won't get you in a cramped area like that but will have you come across some mobs
But yeah.. what I'd do is stealth in there and stealth kill the first guy then run up to the stairs and wait til they stop searching for you, and go for the next (headshots are very good and will probably get you a one shot kill if you have a good gun. This is why I kinda disagree with the advice of some one to ignore gun nut... being able to make a good gun at the beginning will help a lot cause one shot kills are more important in survival. Easier to get them to stop searching if you kill the guy who noticed you cause you shot him. They search less if they haven't been shot).
Try to pick them off one by one. And definitely try to pick off the one with the minigun with a headshot (She will get into view if you look through the right door and if you are far enough away she won't notice you looking at her). But if she notices you she probably won't run too fast after you so run far away (like at least to the lobby before the stairs if not the stairs) and then hide and if you are in caution with brackets not right next to it, sneak farther away and then watch the brackets and if they aren't going closer wait until they move farther away and you are hidden again.
Also, in my game and I am betting it will be in yours too, there is a sniper gun you can get on the second floor of the town near Sanctuary (it's one of the buildings on the south edge I believe, overlooking a campfire and some mattresses. It's on the second floor by a skeleton and I'm betting it's always a sniper rifle cause it looks like one of those set up by the developers as telling a story through placement of skeletons/items). A good sniper gun will really help you to get those one shot kills from far enough away they won't outright notice you (but put you in caution) when you shoot some one.