Newbie needs polishing help

I am making bracelets for my daughters using silver and gold filled
wire and silver and gold filled beads. These are made of 1/2" loops
from the wire and linking them together with the beads. The loops are
soldered shut. Doing fine until the polishing. Taking way too much
time to do by hand and not really getting the finish I want.

I do not have a vibratory tumbler but do have a 1 qt. size
rotary/barrel type. Can this be used to polish items of this type?
If so what type of media should be used? Stone, metal, something
softer? And what should I use for the polishing agent?

Thanks for any and all suggestions or thoughts.

Please reply to @Dave_Bester

Old Abuelo