Help me pick the right stone type for 22k gold collar

[dhimer]

New to colored stones and need your help determining where to focus my search . I would like to add a color stone pendant to my collar ( see pic). It needs to be big as the chain is 4mm in width ( thinking at least 9-10 mm for visual impact). I’m drawn to green ( any green )and red ( pure red, not pink or purple) colors. I’m not picky on the stone shape. My budget is 3k USD. I’m feeling confused on what type of stone to focus my search given my requirements. What I have come across so far that fits the color and budget? is tourmaline, spinnel and tsavorite. Am I missing anything else ? Should I eliminate anything ? Any leads to a stone with links is much appreciated.

 

[Autumn in New England]

So if you need to go large (10mm) and your budget is $3k, I would strike red spinel and tsavorite from the list (unless you're willing to do a cabochon). Pure red gems (if we're talking faceted quality) are some of the most expensive on earth. So I might switch gears to a rubellite (pinkish-red) or a green tourmaline. You can go pretty big and stay on budget. Now if we're talking more translucent cab quality gems, you may find a larger red spinel or tsavorite in that size within your budget. Lovely collar!