Another vote for tumbling and deburring.
I definitely prefer to start out with shiny rings. I make maille and, depending upon the weave, tumbling the finished article just doesn't cut it.
If you're serious when you say that shiny rings hurt your eyes, then you may want to get that checked out - I noticed that I have a tougher time seeing in bright sunlight than I used to and it turns out that I've got the beginnings of cataracts. In the short term, maybe some very lightly tinted glasses may help.