It doesn't matter whether you breathe through your mouth or your nose (other than you might take in a few extra bugs through your mouth). It's the same air and it gets mixed well before it gets to your lungs.

What does matter is that you learn to breathe deeply - using your diaphragm (the muscle below your stomach), not your upper chest muscles.

It's also important that you match your exercise rate to your oxygen intake rate. You want to maximize the burning of blood glucose (aerobic pathway) rather than muscle glycogen (anaerobic). The rule of thumb is that you should be breathing hard, but not so hard that you can't carry on a conversation.

One word of advice for those just starting out on an exercise program: your cardiovascular fitness will improve much faster than your muscle strength. So be careful not to increase your week-to-week workout load too fast, you might end up injured before you get fit. 10% per week is certainly safe, 20% per week is probably ok for most people too.