I'm of the school, "If you're going to wear a necklace, wear a NECKLACE." I have a delicate gold chain with a heart charm - which I wear as a personal item, not a fashion item or completer. If I use a necklace (instead of a scarf), I personally like substantial pearls - round and baroque mixed for the Chanel look, with silk blouses or as a contrast to tees and jeans. I also have a necklace of big (fake) tortoise-shell beads (sort of flat ovals) that look good in the fall with knits and tweeds. Or, instead of a necklace, a big brooch.
When you said, "David Webb," my immediate thought was, "Kenneth Jay Lane" - THE quality costume jewelry designer. Similar shapes, colors, themes as David Webb but affordable! (Affordable being relative of course). From classic pearls (a la Jackie O and Barbara Bush), to natural, animal, deco, nautical, quirky themes. His pieces are sold at major retailers, but you'll see his full range on his own website. He's been around for many decades - there's probably a ton of vintage on resale. Take a little time to explore his website.
https://kennethjaylane.com/collections/necklaces-1
Carolee used to be the best in costume pearls - 30 years ago, alas. Looks like the brand has been resurrected somewhat - there's a limited selection on their website, I can't speak to the quality now.
https://www.carolee.com/
Miriam Haskell, an old costume jewelry brand, has also been resurrected - very unique with pearls, crystals, filigree (and expensive $400-600 for necklaces - each piece hand-made to order).
http://www.miriamhaskell.com/
Alexis Bittar is very modern and fun.
https://www.alexisbittar.com/discover-new