I would suggest starting even finer. 600 grit to start, then see how flat the part actually is. If it requires material removal to come off flat, then go coarser. I would suggest that a 340 or 380 grit be as coarse as you should go, though, otherwise you will spend WAY to much time sanding out scratches from the previous grit.
Keep in mind, if you don't want it polished up like chrome, you can get a nice texture that looks like surface grinding, by carfully sliding the part in one direction. Nice linear pattern!
Use the sandpaper wet (get wet-or-dry sandpaper, usually black color) and use it on a flat surface, like a plate of glass or similar. You can use a flat surfaced block, with paper wrapped around it, too, with the part held securely.
If you hunt around online, you can find the Micro-Mesh brand kits of abrasives, with a series of abrasive sheets going up to about 12000 or 15000 grit. Should run about $30
On steel, these will give a mirror finish, long before you get to the highest grits.
I would advise against going at you gun with a buffer without having some practice first, as it is easy to blur off the edges, and generally make it look pretty poor, if you are not sure of exactly what you are doing with it. If you go up to 2000 grit, I would be surprised if you thought you would need to buff anyways. It'll be really nice at that!
The finer abrasives will give you a very high polish if you progress through the grits in sequence.
If you were planning on bluing the areas after, I would suggest stopping at about 600 or maybe the next grit up, depending on what you like the looks of. Some of the cold blues like to have a bit of "tooth" on the surface, to allow it to finish well.
Cheers
Trev