Working with crystals in terms of the elements is not an area I am overly trained in but it’s something to do further research on. There are many different cultures and philosophy which leads to conflicting information, but for example there is Earth, Air, Fire, Water and Spirit.
Air/wind Stones - Amethyst, Fluorite, Selenite, Labradorite, Sugilite
Fire Stones - Amber, Carnelian, Citrine, Fire Agate, Fire Opal, Red Jasper, Sunstone
Earth Stones - Agate, Jade, Halite, Hematite, Jasper, Jet, Onyx, Obsidian, Black Tourmaline, Garnet, Pyrite
Water Stones - Amethyst, Aquamarine, Moonstone, Blue Lace Agate, Celestite, Chalcedony, Chrysocolla, Pearl, Sea Salt, Selenite, Rose Quartz, Larimar
Spirit / Naisha Ashian has Storm as an element, so it varies: Apophyllite, Danburite, Diamond, Phenacite (Phenakite), Clear Quartz
General guidelines: mix fire with air, and earth with water. IN contrast, combining (FIRE) Carnelian/Citrine and (WATER) Blue Lace Agate, may not be a great combo.
Naisha Ahsian Crystal Ally Cards is a great resource to learn about crystals and the elements.