You definitely do not want to be a heel-striker. If you land on your heels, you are stopping your forward momentum and causing undue stress on your knees. Landing on your toes causes your calves to do too much work, which can lead to shin splints. Running on your toes can also lead to bouncing, which is an inefficient way to run.
To determine what type of footstriker you are, pay attention to which part of foot you're landing on when you're running. If you're a heel-striker or toe-striker, you can try to switch to landing on your mid-sole by not overstriding. Make sure that you don't lunge forward with your feet. Focus on landing on the balls of your feet, with your foot directly underneath your body with every step. A short, low arm swing is the key to keeping your stride short and close to the ground. You can practice changing your footstrike during shorter runs at first, and then work your way up to doing it during longer runs.