With Al’s post, I would like to emphasize that you approach HIIT with caution, especially if you’re thinking about sprinting. It’s extremely taxing if you’re not used to it. Whenever I put them in my programming (which typically lasts for a week or two) the first workout leaves me sore in various ways that I don’t experience with calisthenics. Even if you’re good at pistols it won’t mean that you are necessarily conditioned for sprinting. I only bring this up because I know one of your goals here is to lose fat so I’m not sure how ready you are for that exercise.
But, you asked for the best way to torch fat and build muscle, and my suggestion is an excellent one, especially for someone who doesn’t want to use weights or machines. While sprinting is awesome (kicks your metabolism into hyperdrive, releases significant levels of HGH, great workout for the lower body [especially when utilized in tandem with pistols and bridges]), it is something you need to prep for and so until that point, Al’s simple, direct advice may be the most applicable to you for now.