Finishing Plastic (Sanding?)

Anyone know the best grade or method to finish off plastic? This isnt to paint, so Im after the surface to be as smooth as possible to finish it off

Wet and dry worked quite well, still not as good as I wanted, might have to re-think this!

Its basically a plastic speaker grill, but Ive cut the actual meshed like circle from the centre and want to finish the edge off better. May not need it now as I might run some neon wire round the edge and therefore that should cover it... but then thats my next problem too! Finding something to hold neon wire down tightly round a circular edge!

Too messy and not strong enough! Will sit too proud too, thinking of engraving like a rut round the edge and placing the wire inside that and super gluing it - still not sure it would be enough.

Heres the area Im working on;





Its already alot tidier than those pics though, as I have my new speakers in now, used some smooth sand paper round the edges, and brought the speaker forward on MDF spacers