Kettlebell workouts do a pretty good job of working both power and cardio at the same time, and are pretty efficient at hitting a lot of major muscle groups (posterior chain, core, lats, delts). They have a nice HIIT burn that compares favorably to pure cardio for fat burning. Biggest two kettlebell movements are KB swings for core/legs/posterior, and then something like Clean & Snatch or Clean & Press for shoulders and upper back. For swings you'd probably start at a 42 lber but would jump up to 62lbs+ within a month or two. Snatch or press maybe start at 35 or 42 depending on how much strength training you already do. There are kettlebell complex programs like Armor Building Complex, The Beast or The Giant if you want something more structured. I also like to add in Bulgarian Split Squats to really hammer the quads/glutes/hamstrings, and pullups.
For hitting the ball harder, a couple tee sessions a week gives the biggest bang for the buck I think.