I don't do production work, so have never used a tumbler, and
folks around hear don't seem to go for matte finish, so I don't
do that either.
As for a bright finish, I start with files, only where needed
for major gouges or shaping. Then I graduate to 400 grit
sandpaper, then 600 grit, then I use bobbing compound, followed
by tripoli and finally rouge (gold) or Zam (silver). When using
the sandpaper, I use sanding discs on areas that I can and still
maintain clean lines. Everywhere else I use the sandpaper
wrapped around paint stirrers or popsicle sticks, or anything
else that will fit where I need to go.
I have found that using the bobbing compound before the tripoli,
really gives a mirror finish. If you don't need a "designer"
finish, you could omit that step. I have to admit it is a pain to
keep changeing the buffs for each step and if you are doing
production work, the additional step could add to a few dollars
in labor cost.
Hope this helps.