+1 on Mick Karn, a unique fretless player(with Japan, solo, and various projects with Peter Murphey/Dali's Car, Midge Ure, Bill Nelson, Gary Numan, Kate Bush)
+1 on Paul Raven---Killing Joke's "Night Time" a quintessential 80's album that featured a tune called, oddly enough, 'Eighties', which was heavily borrowed from by Nirvana for 'Come As You Are'; his predecessor, Youth, was no slouch either
+1 on Graham Maby w/Joe Jackson; he navigated lots of Latin style lines when JJ went in that direction
then...
Norman Watt-Roy with Ian Dury, his shining moment was 'Hit Me with Your Rhythm Stick'
Dave Allen, first with Gang Of Four, then Shriekback(who featured a lot of groove/world rhythms); key tune: 'My Spine Is The Bassline'---that just about sums it all up
Sarah Lee, DA's replacement in Go4, played with Robert Fripp for a while before that, then later in the B-52's
Tina Weymouth always had tasty melodic lines in Talking Heads(who also explored world rhythm later on)and Tom Tom Club
JJ Burnel with the Stranglers always had great grindy Entwistle-like lead bass lines on their earlier stuff; they got more synthy as the decade wore on, be he always delivered; key early tracks:'Peaches', 'Nice And Sleezy'(technically 70's, but who's counting?)
Colin Moulding with XTC was a McCartney for the New Wave, perfect melodic lines in very quirky songs
For pure African stuff, do not fail to check Fela Kuti(so many albums, but "Black President" will get you going), and King Sunny Ade(start with the album "Juju"), not to mention the compilation, "Incredible Beat Of Soweto"