Have you just started the game? kill a raider or two and take their amour, or there is a suit of power armer that easy to get just to the south east of the Poseidon energy building,https://www.youtube.com/watch?v=RLSXQvNmMrY
I've got brotherhood armour. I do have a set of power armour that I got at the very beginning of the game. I left it at red rocket garage and came back to it when I found a fusion core and it has been stripped of all its armour plating. Only the frame was left.
Pretty much everything kills me instantly! I had a laser rifle but out of ammo. No weapons shops, very few caps. I'm level 11 I think.
Save up 3000 odd caps and 3 fusion cores. Go to vault 88 and look in the shop for a combat rifle called Overseers Guardian, for every one trigger pull it fires 2 bullets.