I think you can even do it at home, for you to improve speed just jump side by side left and right,
Or set a table( imagine it as table tennis table), then make a large 2 steps from the service side at the left, to the deep inside at the right net. Then go back to original position.
Then change the original position to the right side and going to left side.
You will find them listed in the google page above. You can identify them with the thumbnails with yellow and white text.
I have done some fitness training in the gym. It really helps to work on the legs, back and core muscles. If you just want to build some muscle but not become heavier, then you should do more repetitions with less weights. I do typically 3 sets of 20 for these muscles and gradually increase the weights once I become comfortable with a certain weight.
This has helped me stay lower without getting tired and increase my lower-body stability. I still have a long way to go though.
I use the leg curl machine but not the leg extension machine as it doesn't feel right for my knees. A lot of people online have also been saying that the leg extension machine is not good for the knees. Do your research on this.
You can also do free weight exercises like squats, deadlifts etc. but make sure you ask a trainer or someone who knows what they're doing if your form is correct. Similarly, I see a lot of people using machines wrong. They take a large weight and use their momentum with fast movements to lift larger weights than they should. Lifting slowly with a lighter weight is better and makes you less injury-prone.
You are free to build muscle if you like. It hard to get "too big" and you can always take a step back if you become "too big". However, I would focus more on the lower body and core than the chest and arms as they will help you more in table tennis. Check out the physique of any of the top chinese players like ZJK or Xu Xin.