I am afraid it is not that simple. You are going to apply active vibration control. It includes vibration sensor(s), actuator(s) and control circuits, all the system implementing a good control algorithm. You can refer to Vibration Control for Optomechanical Systems by V.M.Ryaboy, World Scientific, 2021, Chapter 9. ISBN 9789811237331.
choosing the actual board probably should be one of the last items to be handled during system design. What necessarily comes before is
How does your overall control strategy / concept look like?
What kind of sensors do you need to acquire data? What kind of signal conditioning / interface circuitry is required for them?
What kind of actuators do you intend to use? What kind of power amplifiers do they require?
How do you want to deal with A/D and D/A conversions? Mind the anti aliasing / reconstruction low pass filters - they are likely to be key components for your system latency!
Now, we are coming closer to the actual "board": Depending on the frequency range and the overall concept, you will have certain latency requirements. Make sure you select a processor powerful enough for your computational requirements AND a firmware / software environment (in addition to hardware interfaces) allowing you to achieve your latency requirements.
Finally, we arrive at the "board" level: Select a board based on a suitable processor, supporting the firmware / software environment and providing you with the right interfaces for your sensors & actuators.
If you will find Arduino or a likewise platform to be sufficient for these requirements - great! You will get great software support plus an exceptional price / performance ratio. If you will need some DSP eval board, this would also be fine, as they are also often relatively affordable and well supported. If you need a flexible solution with a graphic programming environment and are willing to live with given specs (and likewise with spending more money), go with some commercial offering like NI, dSPACE, etc., on the hardware side - but don't forget to make sure that they really fit all of your needs as outlined above.
If you want to go beyond just a lab environment, please keep in mind that all of this needs to be qualified for your respective environmental (temperature, humidity, corrosive media, shock & vibration, EMC, ....), power and packaging requirements.