Choosing Shipping Carrier

Quick question to seasoned Sellers in the US, specifically those that handle their own fulfillment and have product on the Amazon Marketplace. Also, even more specific if you’re based in California. Who are the shipping carriers you can ship with? Are you able to add additional ones or just stuck with whatever Amazon gives you? Can someone list out which carriers you have options for? Any alternates to UPS, FedEx, USPS? Thanks so much!