Normal router bits + emery/wet and dry work a treat

1/2" round over bit used on 5mm acrylic:

6mm chamfer on 8mm acrylic using large 45 degree chamfer cutter.

3.2mm roundover bit used on 3mm acrylic:

Acrylic cuts fine with regular router bits.
For polishing I start with 180 or 320 grit to remove the machining marks depending on the quality of the finish. Once the machining marks have been removed I normally move up the grades 600 > 800 > 1000/1200 and then use Novus 3, Novus 2 and finally Novus 1.
You can flame polish plastics but I'm not too keen on it. You need to get the machining marks out before you flame polish and by that time you may as well finish it off by hand. Its a little more work hand polishing but its so worth it.
If I'm polishing something flat like that large chamfer above I use a sanding block.
If you are polishing something on a drill arbour/lathe etc you need to keep the revs down to stop the plastic from burning. Somewhere around 300rpm works well for something around 40mm diameter. You can go faster if you can keep the component cool with coolant, airblast etc