Robin2's simple stepper program tutorial may have information of interest.
To achieve higher speeds you will need to accelerate the motor. It cannot reach those speeds from a dead stop. Use the AccelStepper or the MobaTools stepper libraries. I think MobaTools easier to learn.
The Stepper library that comes with the Arduino IDE will not support step/dir type drivers like the TNC2208, TMC2209, A4988, DRV8825, ...