Personal trainer here: Exercise can help, especially if you are not very active. But you can’t out exercise a bad diet. Diet is primary.
Focus on strength training to build muscle, that’s how you increase your metabolism.
You have two options for cardio: low intensity steady state (extended time walking, cycling, elliptical machine. Aim for heart rate 50-75% of heart rate max) or high intensity interval training (short bouts of high heart rate alternated with shorter bouts of recovery, look at Tabata). If you want to do cardio, do HIIT AFTER strength training or LISS on alternate days. If you’re feeling fatigued, listen to your body. Dog walking is a good form of LISS which is good for stress relief and lowering cortisol levels.
Heart rate max: 220-your age.
Tabata: 20 seconds of working as hard as absolutely possible alternating with 10 seconds of recovery for 8 rounds, do as many sets of 8 rounds as your fitness level allows, start with one set and work up. Rest 1 min between sets.
Exercises to do Tabata: kettle bell swings (look at you tube for videos by Pave Tsatsouline for instruction on proper form); medicine ball slams; mountain climbers (modify for your fitness level); battle ropes (you tube videos for instruction); high knees, jump rope, side steps, anything that gets your heart rate up quickly.
Good luck!