New Orleans unique musical heritage was largely self contained and there was no national distributor of classic NOLA records during the golden age of the 50s & 60s that was based in Louisiana. There were national break out records but many hugely popular NOLA artists such Tommy Ridgley never had a national hit. The legacy is a myriad of small label releases that to this day have stayed in New Orleans and the environs. I've been collecting them for years and am still finding uncatalogued material.
Here are some excellent compilations on silver disc. I'll mention a few that haven't been yet. The 'Gumbo Stew ' set of three mentioned above are outstanding IMO.
Orleans Record Story - 90s compilation of contemporary material Orleans label
Crescent City Funk - UK Grapevine (2002)
Chess New Orleans - classic era from the likes of : Clifton Chenier, Eddie Bo, Edgar Blanchard, Earl King, Frogman Henry. - Double Cd of Chess label releases.
Amy/Sansu compilation: Get Low Down: The Soul of New Orleans '65 - 67
Watch records retro inc: Johnny Adams, Tommy Ridgley, Benny Spellman, Professor Longhair, Mardi Gras records (2000) - contains cuts on CD that are difficult to find anywaher.
New Orleans Funk 1960 - 1975 "CD collection from UK Soul Jazz
Vin label story: New Orleans R&B and Blues; Elton Anderson, Huey Smith, Jimmy Clanton, Dicky Williams Demon 2000
Lanor Records Story 1960-1992: A retro of Louisiana based artists inc: Charles Mann, Hugh Boynton. Zane records
Louisiana Gumbo features Charles Sheffield 'It's Your Voodoo Working', Snooks Eaglin, Putumayo (2000)
The NOLA greats are very well covered for CD/LP retrospectives (Percy Mayfield, Clifton Chenier, Irma Thomas, Allen Toussaint, The Meters, Little Richard et al) but you might also want to become familiar with some of the lesser known artists who are part of the story. I'll highlight the following six:
Theryl ' Houseman' de Clouet : The Houseman Cometh (2001) / The Truth is Out (2007) Rounder records
John Boutte: You probably need just the one so 'Good Neighbour' album is recommended. It contains the theme song for 'Treme' incidentally.
Sam Montel presents The Boogie Kings - A collection of Jin tunes. Not essential but fun
Vasti Jackson - New Orleans : Rhythm, Soul, Blues (2013) - New stuff paying homage.
There are at least two good Eddie Bo retrospectives easily available
C.P.Love - Eponymous LP from 2000 Orleans records /Vivid Sound Japan - short but sweet.
So much more I could say and add. Love me some NOLA tunes!