I went to see a bluegrass band with a friend of mine on Sunday called Dailey and Vincent- as a guy who's never really listened to much bluegrass [and definitely never heard it live], I really loved it. If you've never heard of them, I'd def check them out!
As for blues, what sort? If you're into blues rock, Clapton would be my first choice. His entire discography is pretty good, imo, especially the 70s stuff, as well as his collabs with other artists. But Robert Johnson is also a favourite of mine.
Big Bill Broonzy - Hey Hey [link] Mississippi John Hurt - Make Me Down a Pallet on Your Floor [link] Skip James - Crow James [link] Blind Willie McTell - Statesboro Blues [link] Barbecue Bob - Motherless Chile Blues [link] Big Mama Thornton - Wade in the Water [link] Elmore James - Dust My Broom [link] Sonny Terry & Brownie McGhee - Hootin' Blues [link] Lonnie Johnson - Too Late to Cry [link] Peg Leg Sam - Born for Hard Luck (not a song, but a great clip) [link] Ella Jenkins - Racing with the Sun [link] Mississippi Fred McDowell - Shake 'Em On Down [link] John Lee Hooker - Boom Boom [link] Son House - Grinnin' in Your Face [link] Howlin' Wolf - Smokestack Lightnin' [link] Lead Belly - Midnight Special [link] Lightnin' Hopkins - Baby Please Don't Go [link] Taj Mahal - [link] Blind Blake - That Will Happen No More [link]
a few more modern day bluesmen:
Alvin Youngblood Hart - Illinois Blues [link] Gary Clark Jr. - Next Door Neighbour Blues [link] Guy Davis - Hooking Bull at the Landing [link] Corey Harris - Honeysuckle [link] Pokey LaFarge & the South City Three - Head to Toe [link]
This is just for starters! I've tried to link to live footage where possible. Enjoy!
I don't know much about bluegrass, but when it comes to the blues, I think you need to hear Muddy Waters first. The Definitive Collection's got all his big hits, like Hoochie Coochie Man, which you might recognize from Goodfellas, and Rollin' Stone (where a certain band got their name from). It is one of my few desert island albums. Then there's Robert Johnson. Ever heard of the 27 Club and the deal-with-the-devil-at-the-crossroads-in-exchange-for-your-soul legend? That's him. There's so much amazing music, but I can't give links to 50 musicians and expect you to actually listen to them all. I say start with old Muddy Waters, and if you like that then go on to the rest of 'em.