You'll be able to find many composed rounds and some traditional ones.
Madrigals: These are generally the most difficult. Get your better singers on these first. What we do with the King's Chorus in Atenveldt is get a group of four or five singers who can read music and are confident enough to sing one-on-a-part, and have them learn a madrigal well and memorize it. Then we make enough copies of the song for everyone in the larger group, and teach them all. This way there's at least one person in each group who knows the song very well and can be a sort of section leader.
Most madrigals are Renaissance or Elizabethan pieces.
Ballads: Traditional ballads are narrative songs; they tell stories. They're not really intended for group-sings, but certain ones will work in groups, particularly those with refrains.
Ballad singers come in varying degrees of purism. I myself like to make sure that both my words and tunes are traditional. There are many books and recordings available. The main text reference on English-language ballads is The English and Scottish Popular ballads, edited by Francis James Child.
Part Songs: Part songs are generally easier than madrigals because the different sections of the chorus enter together and sing the same words at the same time (unlike madrigals, where the words may never come together).
Check hymnals for older hymns. They're good practice!
Folk Songs: Traditional songs that won't fit into any of the other categories must go here. There are cumulative songs, such as "The Twelve Days of Christmas" and "The Rattlin' Bog," which are great fun, rowdy, and easy to pick, up. By the end of the song, the whole audience is singing!
Songs like "We Be Soldiers Three," "Three Jolly Coachmen," and "A-Roving" are classified as folk songs because they're traditional and can't be classified as ballads.
"Filk" Songs: These are all post-A.S.I, and you might consider that "period." I don't know how widespread the term "filk" is. It refers to SCA ballads written to the tunes of modern songs (show tunes, rock'n'roll, American ballad tunes, etc.).
Although I myself much prefer 'real' ballads, I have been known to listen attentively to, laugh with, and even sing filk songs. These are more popular in some areas than in others. Sometimes we purists butt in and try to spoil the fun with that old line "It's not period." Ignore it. Sing what you and your audience enjoy.
Plan A: Start by getting a couple of good old rounds.
Next, announce that you're forming a chorus, or madrigal group, or whatever, and that you want people to come and sing even if they've never sung before. (Emphasize that part — some of our best singers had never sung before they sang with us.)
After you've learned a song or two, perform them — anywhere. Fighter practice, a meeting, a revel. . . you'll pick up some more singers after you've been heard. A leader will probably emerge from all this.
Plan B is any other plan you think will work in your area.
If any of your singers have sung in choirs before — in school, church, city groups, whatever — ask them for suggestions on period music. Perhaps they still have a copy of something they've sung before. Make sure it's pre-1600 and then sing!
Here are two books you might look at:
An Anthology of English Medieval and Renaissance Vocal Music, edited by Noah Greenberg. This has forty-seven pieces in chronological order (the first is before 1170 and the last is before 1650). Some of the songs are one-part (unison); there are duets, trios, etc., up to a six-part madrigal. This is a paperback edition published by The Norton Library, W.W. Norton & co., Inc., New York. (The original title was And English Song Book.)
Invitation to Madrigals, Books 1-11, Galaxy Music Corporation (paperbacks). The blurb on the back says, "Graded anthologies of madrigals selected, transcribed and edited from original sources and with prefatory and performing notes by Thurston Dart, David Scott and others. Most of the series is taken from the greatest period of the madrigal: England in the 16th century."
When this article was written, for the first Known World Handbook, the author was a Companion of the Light of Atenveldt (the Kingdom service award), and was serving as Kingdom Seneschal. She is now a Viscountess and a member of both the Order of the Pelican and the Order of the Laurel. Sandra Dodd is a former teacher, just completing a term as Steward of the SCA.