2channel8: If you want to start with an album of just Gillian and her guitarist/harmony singer David Rawlings, The Harrow & The Harvest is the one. All the songs on the album were written by Gillian and David, and the album was Grammy-nominated for Best Engineered Album (non Classical) and Best Folk Album.
If you want some instrumental accompaniment, on Soul Journey the duo adds a few real fine musicians, they being Greg Leisz on dobro, Jim Boquist on bass (like some other well-intentioned but mistaken folks---including John Atkinson, his instrument is listed as bass "guitar". There is no such instrument---a bass is either a standup/upright acoustic or an electric, unless you are speaking of the early-1960's Fender 6.), Mark Ambrose on acoustic guitar, and Ketcham Secor on fiddle. Again, all songs written by Gillian and David.
And then there is the All The Good Times Are Past & Gone, Gillian and David's album of covers. Songs written by Elizabeth Cotton, Bob Dylan, John Prine, Norman Blake, a few others, as well as some written by "Traditional" ;-) . Arranged by Gillian and David, produced by David. On the inner sleeve the recording equipment is listed, and it's impressive: Telefunken mic, tube Studer tape deck, the lacquer cut direct master tape to a Neumann lathe with an Ortofon cutterhead. Yeah, baby!
If you like the above enough, there is a 3-LP boxset entitled The Lost Songs/Boots No.2. One great thing about the duo's Acony Records label is that the LP's are more modestly priced than those of Analogue Productions, Speakers Corner, MoFi, Intervention, etc., at around $30 a disc. Gillian and David, cool people!