You don't mention volumes, but you could pilot from both sides then finish straight thou.
Also solid carbide mills will deflect less.
We index the parts in these operations.
Joker
It really depends on what type of plastic. But generally you should use a 2 flute endmill. Lots of coolant. Run your spindle as high as you can . Feed about .010" chip load.This should give you at least a 125RMS finish.
Good luck