I don't know what machines are available in the EU. Given the resolution and accuracy you want, finding a machine in your price range might be difficult. That is not normally something you find in the hobby class machines. A used commercial machine might be your best option. If you can find one that is in mechanically good condition with bad controls, upgrading the controls is not that difficult expensive. I'm not sure if a stepper driven machine will give the resolution that you want, maybe if the motors are geared down it would work.

EDIT:
Maybe something like this?