If you aren't interested in investing a lot in your finishing tools but want something better than what you can accomplish by hand, I recommend a tumbler.
Handmade Jewelry - Valeriy Vorobev - Handmade wire jewelry. Wire
Adam and Karen Fifield - Mattoon Area Family YMCA
DIY Handheld Jewelry Tumbler Polisher
VIDEO: How to Use a Tumbler in Jewelry Making - PKlein Jewelry Design
Semi-Automated Jewellery Polishing - Vibratory Tumblers
How to Polish Jewellery Using a Tumbler
Jewelry Tumbling and Sorting Tip
Zen Spiral Pendant Tutorial – Jewelry Making Journal
Jewelry Making Class: Cage Wrapping Seattle, Gifts