I think the ideal regiment is 4x a week -that way you can do an upper/low body split twice a week.
However since you play alot that would be too much. I'd do two full body workouts twice a week. I find that only once a week it seems like you won't make enough progress for it to seem worthwhile.
So do two fully body workouts twice a week - but they have to be spread out a few days.. I think this will give you the flexibility you need with tennis.
So maybe Mon Thurs for example..
Might look like this:
Push: Neutral Grip Dumbell Press, or Bench Press
Pull: Seated Row or Dumbell Rows and Pulldowns/Pullups
Knee Dominant: Squats or Romanian Split Squats or Single Leg Leg Press
Hip Dominant: Deadlifts or Romanian Deadlifts or 45 Degree Back Raise.
With a limited regimen like that you can fit in some 'pre-hab' work like the throwers ten that was recommended here..which is nice for your shoulder.
I like Y's and T's as well as some rotator cuff work - instead of the whole throwers ten..but YMMV.
This is not ideal for bodybuilding purposes because you will eventually start to see lagging muscles (say calves for example) but for fitness/tennis purposes a few multi-joint exercises twice a week is enough..