As a precurser to the genres you mention, I would highly recommend learning some Motown. Some of it can be pretty complicated but a lot of it is great for beginners. Also the basslines aren't as hidden under the other instruments as some newer stuff. It gives you a great understanding of chords and bassline construction.
Dock of the Bay, Heard it Through the Grapevine, Lovely Day (Bill Withers), Lean on Me, Stand by Me, are ones that come to mind at first. I'd say learn the overall groove with root notes then work on the embellishments.