Are we at a place already that we can discuss designers by century, and not decade? 
Nitpicking aside, a good place to start is actually not with designers, but architects. For some reason, they usually produce way cooler furniture than designers. Ludwig Mies van der Rohe, Alvar Aalto, Charles Rennie Mackintosh, Le Corbusier…
Either search for those names, or simply Bauhaus. Both should produce good results and are good starting points.
(In college, my teacher preferred to start the “design era” with the Shakers, but I’m still not convinced about that… to me, that’s still crafts, so it depends on where you draw the line…)