Running out of breath is something that'll improve over time. Your body can only extract so much oxygen from the air you breathe, this gets better as you get to your heartbeat rate up more frequently. No worries.
Back in the day when I went to the gym, I was told that optimum heartbeat rate for burning calories (cardio training is what they call it) is 85 percent of 220 minus your age. So if you're 30, this works out at (220-30)*0.85 = 161.5 bpm. Is this rule still being used today?