What you are experiencing is very common, and almost a classic anxiety symptom. I have this problem myself from time to time, getting heavy palpitations early during exercise. I can 100% relay to your problems.
Palpitations during exercise are usually caused by premature atrial contractions (PACs) in other words normal heartbeats that origin somewhere close to your natural "pacemaker".They are conducted through your heart through normal pathways, they do not reduce your cardiac output, and they are essentially completely benign.
When you start exercise, you will get elevated adrenaline levels, and with a somewhat high "baseline" adrenaline level due to anxiety (and especially if you have this on your mind and expect them) will make your heart do some extra beats. It usually settles later during exercise when adrenaline levels are more normal, you are reassured, feeling "this wasn't so bad after all, I survived, etc.)
It's fairly normal get aware of palpitations when resting, between panic attacks (panic attacks usually cause sinus tachycardia, normal high heart rate, or the skipped/double beats just disappears in the mess a panic attack can create). I'm famliar with this problem, too.
I agree with debbier's answer, it's a good idea to see your doctor and get the necessary tests done, just to rule out any problems and, more important, get this out of your mind.
What I maybe disagree, is this being PVCs. Palpitations during exercise are usually PACs.
Good for you for making a change and getting healthy, I would definetly check with a dr, maybe wearing a holter monitor for a few days while you excercise will give the dr the information you need. It could be now that your moving and getting your heart rate up your more aware of your heart rate and feel the pvc's more. Good Luck!