I have vertical curtains (they go up and down pulling a cord)
Any advice which best hardware integrates the best with Home Assistant?
An ESP device with ESPhome is probably the easiest to integrate into HA.
You just need a stepper driver än stepper motor and the issue will probably be the stepper motor.
You need one tht have the torque to actually pull your curtain up, which can be hard to find.
You can increase the torque with a gearbox, but that lowers the speed and usually the speed gets too low before the torque gets high enough.
You also might need a good amount of holding torque, so you can turn off the motor when the curtain should not be moved.
This usually requires a stepper motor with permanent magnets, which might affect the power requirements of the stepper driver.
Without an adequate holding torque your curtain will just roll down when the motor is turned off and keeping the motor on will make it draw power all the time and it will be hot and probably eventually burn out.