Since the Sun is so much bigger than every other object in the Solar System, and dominates the sky... it makes sense to me to make it at least a little bit bigger than the other planets (technically of course, the sun is a "luminary" and not a planet..., but in astrology it's often referred to as a planet).
Since the Sun's symbol in Astrology is a circle with a dot in it... See the big bright yellow bead in the picture... That's the bead representing the sun Sun...using a donut bead (with a carnelian center bead).
If you are a fire sun sign - probably - if that's what you like... otherwise, maybe. I like to go over the whole chart with you to decide what is going to make you the happiest with the finished piece. Polarity, Modality, and Dignity might also come into play for the final decision.
Perhaps you just have an affinity for a particular bead or stone... and you want that to be your sun bead. Cool with me. As long as it pleases you. There are no rules here, on selecting certain gemstones or beads for whatever you want.
These are beads I have used, and like to use, for Sun beads. Most are larger beads. Any bead could be used to represent the sun, if it appeals to you. I tend to go for the larger beads, as a default, or something like "Sunstone" or fiery looking beads. Sometimes we go with what time you were born, or if there was an eclipse that day, to signify that astrological aspect of your natal chart.
I have quite a few in stock, Red Jasper, Howlite, and the yellow Calcite pictured above, also several other large (over 1.5" in diameter) as well as smaller ones.
If it's obviously the biggest bead, then it's pretty clear what it is. If you go for a similarly-sized Moon bead, then it won't be so obvious. Tiger's Eye and Clear Quartz (pictured above) make nice Sun beads. But so does Sunstone and many other stones. There are lots of options.
Like dark-colored beads? Born at night, or during an eclipse... Why not Black Onyx (or whatever) for the sun, if you like it?
Above is Ian's necklace with his Rhyolite donut Sun with a Tiger's Eye center, conjunct his Ascendant (Howlite triangle bead) conjunct his South Node (gray moonstone).
I keep buying new beads, and when I find a nice big one, I have to have it... it's fairly rare to find such big beads, but they make awesome Sun beads. Larimar is associated with the Zodiac sign Leo, so why not a Larimar Sun (which rules Leo)? No rules!
I love to see my clients look at the beads they are choosing for their custom horoscope jewelry. It is literally like watching kids in a candy store. I feel the same way. How to decide? As a triple Libra, it's even worse...