You'll need wet & dry paper, probably from a Paint Centre type retailer especially one who caters to the car industry as they use a lot of w&d when rubbing down cars for painting.
I start with 800, then 1200, then 1800 and finish up with 2000.
Don't be caught up in the "mirror finish" thing, you're aiming for a flat surface not a mirror. I test using a razor blade on edge.