After watching my son start out on Pokemon Go and then downloading it myself, I was able to formulate an idea of how I wanted the game to go in the early rounds. While he hit level 13 today and I advanced to level 5, our ways of approaching the game have been very different.
My suggestion is you go after every Pokemon you can in the early stages, but be conservative with the Poke Balls, especially if you do not have multiple PokeStops nearby. We ran into this problem on his game multiple times during a weekend trip but lucky for him, we ended up in a heavily-populated metropolitan suburb in Ohio which was heavy on parks and landmarks, and thus, PokeStops. There he could replenish his Poke Ball inventory, and, while he took a break to play on the playground with his little sister, his mom and I helped him out a small bit to ensure he was well-stocked on Poke Balls.