I would sell the silver to someone that buys metal by weight.

I also inherited a lot of jewelry. For fine jewelry, you might consider how your could reset some of the stones or turn a piece into earrings or a pendant, etc. You won't get the value it's worth if you sell, so try to reuse it if you can. A good jeweler can help.

You could try to sell some pieces online at Poshmark or eBay. I was surprised at what people bought at reasonable prices. Do some research and figure out a fair prices. Don't be greedy or it won't sell. If it doesn't sell on one website, try the other one.

If you have precious metals that you want to melt down, consider this company that I have used successfully multiple times. Read the instructions. https://www.midwestrefineries.com/

... the silver that's tarnished and not my style - where is the best place to sell it for the value of the metal, by weight? (And how does that work? Some of it has semi-precious stones embedded - do they just remove those?)

... the costume jewelry that's not my style but has some (very modest) value - what is the best way to sell it? FB Marketplace or eBay or Etsy... or somewhere else?

There is a lot that I'll just donate but there are some nice pieces that I'll never wear but would like to make some money on.