About how much would it cost to ship a small item (like a ring or necklace, not in a case) through USPS?

I work at a USPS mail processing facility, and if you're planning to send a small item like a ring or a necklace, do NOT try to save money on postage by sending your item in a regular paper envelope. Paper envelopes were designed to carry soft, flexible PAPER letters in them, not hard, solid items like rings, keys, and necklaces. The machines we use to process and prepare mail in paper envelopes for delivery was designed ONLY for paper. Anything harder than a credit card will get stuck in the machine while your envelope gets torn to pieces. Every single day I go to work I find things people try to send that never get delivered because they thought a regular paper envelope was sufficient, but once they go through the high speed machines we use, the items get jammed in the gears of the machine and the envelopes (along with the addresses written on them) get DESTROYED: Keys, coins, name badges, thumbdrives, souvenir pins, magnets, necklaces, earrings, bracelets, etc.

Here's a 53-second video of what the machine looks like and how it works:

https://www.youtube.com/watch?v=AQfFXcp4H6I

If you're going to send a ring or necklace, go ahead and spend the extra two dollars or whatever and put it in a tiny box or at least a proper bubble wrap shipping envelope. It's NOT worth trying to save a few bucks if there's a high risk your item will never leave the post office since we can't identify who it belongs to or where it's supposed to get sent. Boxes and bubble wrap envelopes go through a different machine with that handles packages better.

PS: Writing "process by hand only" or "non-machinable" on a regular paper envelope makes almost ZERO difference. There are millions of envelopes that have to be prepared for mailing every day. Pretty much no one has time to go through the hundreds of thousands of pieces mail we do every single hour to see which ones have are not supposed to be run through the machines. Practically EVERYTHING goes through the machine.

Depends on how much the whole package weighs.

47 cents for the first ounce 21 cents for each additional ounce.