I have a lifting plan, but nothing to work off the fat, "cardio"
I wouldn't do starting strength while cutting calories. Wait until you start a bulking program first, as the program is meant to use progressive resistance training; increasing the weight each session. This is hard to do during a caloric deficit.
As mentioned, the ketogenic diet would probably be your best bet. I've used it for years during cutting phases and found nothing but amazing results from it as have others on this board. The secret is putting your body into a state of ketosis, where it burns fat for fuel. You'll have to do your own research on the diet, but believe me the principles are easily followed.
As far as cardio, nothing speeds up your metabolism like HIIT or any other form of cardio utilizing the anaerobic glysosis - tabata, HIIT, tire flipping or even circuit training. I would utilize the ketogenic diet and do HIIT twice per week for maximal results.
In regards to a lifting routine, it really depends on your level of training. I would focus on a full body program training compound movements and focusing on progressive overload. Increase your protein intake to prevent becoming catabolic and make sure to continue lifting heavy, so that your body has a reason to maintain its current muscle mass; with the keto diet, maintaining muscle isn't an issue at all.
I would also consider investing in some BCAA's. Your bodyfat% is entirely up to you. I like to stay under 10-12%, but that's just me. If you're not satisfied, then cut some more weight. Cutting out carbs with the keto alone will results in some weight loss (water weight), but you'll still need carbs to fuel your workouts, which is where the carb up day comes in with the CKD.
Anyway, good luck. Apply the knowledge that's been given to you and I'm sure you'll do fine.