Not every Shipyard sells all types of ships. You'll likely find less ships in smaller population systems, and more in larger populations. You'll also find less in Agriculture systems, and more in Industrial / High Tech.
Prices are uniform, so it shouldn't matter where you buy. Scroll through the ships on offer.
Options to buy include trade-in value of current ship, or just outright buy the new one - in which case your existing Sidewinder goes into a 'garage' storage at that system and you can return to it later, so a key decision on where to buy is where do you want to store the older ship.
I've read on these boards that trade in values might be 90% of purchase price, and therefore seen recommended to individually sell components (e.g. weapons) back through Outfitters (which I think gives 100% of purchase price), and then finally trade in the empty shell of the ship for the next one.
Bear in mind, when looking at finances, that a bigger ship will need more in credit reserves for insurance cover; bigger cargo holds cost more to fill with commodities; outfitting modules cost more.