You could either do something low intensity like walking for longer periods (I recommend this, less of a cortisol spike, will relieve stress)

or do something high intensity like jump roping/running for shorter periods (this will raise cortisol, but also beneficial to get your heart rate up)

If you're just starting out you'll need to experiment to find what works for you. Don't focus on "what burns the most calories", instead find what is most sustainable and practical for you to do as an every day activity.

 

Depends on if you wanna use equipment or not.

Running is probably my favorite exercising (besides dancing). No equipment needed, you get your cardio in, get to spend times outdoors, you get "runners high" if you do it long enough, it relieves stress and releases feel-good hormones, and the more energy you put in it the more calories you burn. Just be careful not to overdue it and use proper runners form. There's a risk of hurting your knees if you overdue it.

Using a stairmaster burns a TON of calories too, if you have access to one.