Only 3" X 4", it really looks quite bigger than that. At that size a display piece is perfect so a good high polish is in order.
Sandpaper, here's the turners dilemma. The way we use it, at high speed and probably much hotter than other users means most sandpapers (really called abrasive papers) are not able to stand up to our use. And worse still, we are such a small part of any market there is no requirement for a manufacturer to make something to suit our needs. So we've had to discover the best ones for turning of the multitudes available.
There will be some addition or disagreement on these but generally they are some of the best. What you can't source locally I'm sure the AWGB Corporate members can provide at a discount (
http://www.awgb.co.uk/corporate.php);
J weight Cloth Backed - various makers;
Abronet (made by Mirka);
Rhino (Company Name) Abrasives (also available velcro backed).
As for the cutting particles, they can be (in old days) crushed Glass (Sandpaper), Emory (Wet & Dry), Garnet, Aluminium oxides, Silicon Oxides and more. We woodworkers tend to stick to the various oxide versions.
So you are able to remount an sand down to 600. Stop every grit and handsand where necessary getting it right before moving to the next lower grit. Then work through the dampening and cutting back the grain as in the link I put up earlier.
Definitely use the sanding sealer once your happy with the sanding, buff that back with some shavings as it will start the shine and then from what you have I'd use the friction polish. Just don't get any of it on the natural edge as you'll not be able to buff that up!