I'd recommend going down the hill behind the gas station where you meet the dog. You can find another power core for your power armor. I'd also recommend using that has station as your base. It has a rack for your armor in the garage. You might want to leave the power armor there until you get a few more power cores for it. And if you don't care about the main story, you can ignore it. Although, it does start to pick up after you reach Diamond City.

A load of doing things yourself? What's so hard about that?? Look.. Red Rocket Gas Station. First place where you find your dog.. Make that your base. Enough scrap to build basic walls and all that, along with containers for your respective items (ie weapons, apparel, aid, etc). Initially, grab a reasonable amount of everything. No, not every can and fan you stumble across. More like 2 to 3 cans and the occasional fan, asking that rate. You can check your Pip Boy to see what items break down into what components. Check your carry weight as you play. Bring the weapons and armor you use, nothing extra. Bullets weigh nothing, and the more strength you have the more you can carry. That powersuit can be stored at the gas station as well. It will not disappear when you leave, and there is even a powersuit station IB the garage. When you see that you are near carrying capacity, check to see if you have any weapons or armor you aren't really using. Unless it's something really rare (make your dog carry it), dump it. Go back to the gas station, store all your junk in the workbench, and every station you use on the property will pull needed parts from the junk in your workbench. Later, you can greatly lessen the need for all that by getting certain perks. They allow you to dismantle weapons and armor for the rarer components you currently get from heavy junk you pick up. Things like screws and crystals can be attained en masse from weapons and armor now!