For those, who is having troubles with fight system... Firstly, keep in mind, that you're a girl, who just came out the vault, having no experience whatsoever at fighting whatever awaits you outside the vault.
If you choose str as starting trait, you have somewhat decent fighting skills in melee.
I dealt with rats and rad scorpion without any issues with my rusty knife.
There is also a little minigame, that randomly appears during your turn, when you attack, which, if activated at the right moment, deals a lot of damage.
Also, you're supposed to visit security officer, who will provide you with gear and give you briefing about the mission.
I've got a police baton based on class chosen at the start of the game. And you get the pistol no matter if you choose "Talent" or not.
Also, I visited that officer AFTER I've cleared out most of the cave. Two stimpacks were enough for me, so I don't feel like fighting system is a pain in the ass. I'm not trying to sound cool and mock people, because they can't deal with rats, just trying to give some tips.