There is none really. Body fat gain or loss is a question of nutrition rather than exercise.
Regular cardio is a losing battle but strength training will help in some respect since the process of building muscle burns calories and having active muscle mass burns additional calories on its own.
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And don’t worry about becoming bulky… you won’t xD
Nobody has ever built tons of muscle by accident. Just train like you’re trying to.
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As for exercises: well you can do almost anything at home with a bench, a pullup bar, a pair of dumbbells, a bar bell and a decent number of plates.
You should definitely focus on the core strength training compound exercises:
Deadlifts, squats, bench press, overhead press, pull ups/bent over rows
Try to get progressively stronger in those exercises by following a well structured strength building program.
Within a couple of months of decent progress you’ll notice that your body gets more in shape.
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On the nutrition side you should aim to get in at least the amount of 1 gramm of protein per pound of body weight. You can try to cut simultaneously but I wouldn’t recommend it in the beginning while you’re still trying to build up strength.
But you can. Just aim for a moderate calorie deficite of 200-300 kcal per day.
Try doing 3 minutes of burpees everyday for a month and see if that makes a visible difference. Try body weight exercises, HITT or calisthenics. No equipment to buy & can be done at home. Start out with a few minutes per day and increase as you become stronger. There are lots of videos on YouTube.