Plastidip isn't a bad idea.
To answer your questions though; given that it's plastic I'd be careful not to use too course of a grit and mar it up, then it'll take a lot more sanding with finer grit to remove the course grit sandlines. So, I'd probably start with 220 to remove the old finish, it'll take a bit longer, but less risk of scaring it. Then move to 400 and then 600 grit. That should be good to paint on, but if you lay down a coat or two and see sandlines, you can always let it dry and then hit it with some 800 grit to remove any final imperfections before your final coat(s). CTC used to sell a variety pack of wet/dry sand paper in the automotive section with 400/600/800, which would be a good option instead of having to buy each separately.
You shouldn't need to clear coat it if you use a quality automotive rated paint. If you did clear coat it, you'd need to find a semi-gloss clear, as using regular clear on top of a matte finish paint is going to give you a high-gloss.