Julie, are you talking about an informal singing group that gets together to sing for themselves or a performing group?

Also, are you interested more in pop-folk, like the groups you mentioned, or the 'hard stuff' (i.e. the real TRADITIONAL music, or even some of the old-time country music, or blues). If the latter I can suggest a few places to start.

The Anthology of American Folk Music, edited by Harry Smith, recently released a a CD boxed set. This might well be the most influential compilation in terms of the number of people it has introduced to broad spectrum of american folk music.

Will the Circle be Unbroken? Nitty Gritty Dirt Band (with a galaxy of great old time artists, including Maybelle Carter, Doc Watson, Roy Acuff, Merle Travis, et al). This two CD set, originally released in 1972, is NGDB's love letter to the great musicians that came before them. Subtitled Its a raw studio recording cum jam session with NGDB and their muscial heroes playing 38 classic old time songs. Its full of classics like Wildwood Flower, Nine Pound Hammer, Dark as a Dungeon, Honky Tonk Blues, Tennesee Stud, etc. It also includes the chat between the musicians in between takes.

If blues is your thing, go to your local library and check their CD library for Mississippi John Hurt, Robert Johnson, Leadbelly, Blind Blake, Blind Lemon Jefferson, Big Bill Broozny, Tommy Johnson, Sonny Terry and Brownie McGhee.

Burl Ives recordings are good too. As are Pete Seeger and The Weavers.

If you want to get into Sea Songs and Shanties, the Quintessential seminal CD is Songs of the Sea by A.L. Lloyd and Ewan McColl.

One thing I'll mention, albeit reluctantly is the famous fake book 'Rise Up Singing', and it's separately purchaseable teaching tapes. I highly recommend the book as good on-hand reference, given its low price and lyrics for about 1000 songs. (Warning: you will find some people on this forum despise it for various reasons, particularly for its having become a defacto 'folk hymnal'). My reluctance to recommend the tapes stems from second hand reports on their quality. Apparently they are of a single unaccompanied voice and only impart the melody, not how the song should sound (if that makes any sense). Also they are a little expensive, and each tape covers only a small fraction of the book.