A stepper is unlikely to be the correct choice for driving a tool bit. Among other things 300rpm is quite fast for a stepper motor. And they are likely to be too "jerky" to give a good finish. A regular DC motor with reduction gearing would be much more suitable. Machine tools with speed control usually have a system to maintain a constant speed as the load on the tool changes. That probably requires some sort of feedback mechanism.Can you provide a link to the Unimat tool you have?Can you explain in more detail what you want to do. Your comment about the 12000 rpm motor probably has nothing to do with multiple axis control so the whole post is a bit confusing. This is essential before any guidance about types of motor etc can be given.
You will need stepper motors if you plan to control tool positions and you should use proper stepper motor drivers such as the Pololu A4988 (which may or may not suit your motors).A Mega or Uno can easily control 3 axes but a lot may depend on how much computation is needed to interpret the movement instructions. Are you aware of GRBL (use Google).
The MKIII Uno is in the last place you left it (unless you employ a cleaner)....R
Cnc routing of acrylic can be difficult to get acceptable results and tool coolant is essential.Post routing the acrylic will also need annealing, especially if you want to glue it.