Which frequency is the best for a 3-speed Motor?
At or below base motor speed, a motor will operate as a constant torque device. When you use a VFD to operate a motor at above the base motor speed, the motor operates as a "constant power" device, because the amount of torque it can produce is related to the ratio of voltage and frequency, and the VFD cannot create more voltage. So as frequency increases, the ratio goes down and so does the torque. So with a 970 RPM motor forced forced to run at 1000 RPM by increasing only the frequency to 51.5Hz, the operating torque the motor is capable of will only drop to 97% of rated, basically still within "normal" tolerance range (assuming +-10%).

But if you use the 700 RPM connection and increase the frequency to 71.4 Hz in order to get 1000 RPM, the motor shaft torque will be decreased to 70% of rated torque and if you use the 350 RPM connection and increase the frequency to 142.9Hz to get to 1000 RPM, the motor will only have 35% of rated torque at best. In reality in both of these scenarios the actual usable torque will be even LESS because losses in the motor will increase and cause the motor to overload faster than normal. Then to make matters worse, the PEAK torque, called the "Break Down Torque" that the motor uses to RE-ACCELERATE a motor after a change in loading, reduces by the SQUARE of the change in the V/Hz ratio. So the likelihood of stalling the motor when a load is applied increases exponentially.

Use the highest speed.