I think most has been said, but from personal experience I can only agree wholeheartedly.
I have been running 18-20 miles a week for close to a year. This helped me shed some pounds and build endurance, but it also made me noticeably sluggish on court.
A year ago I changed my whole approach by working out 3x / week, focusing 95% on Core strength and HIIT (boosting Agility, Explosiveness, lateral movement) and 5% on Shoulders/Back Strengthening, Stretching. The change has been, simply put, phenomenal.
My reaction time, balance and explosiveness on court has been the best its ever been. I added a few mph on my serve and groundstrokes, and I have been injured less. The Best part was that within 2-3 Months I could see a difference already.
I suggest you find a class in your local gym that provides this regimen to make motivation easier and your gym time as efficient as possible.