In the LionBrand.com Learning Center, we recommend the knitted cast-on as a good basic cast-on for beginners to learn (because the motions are very similar to making the knit stitch). Other common cast-ons that are used by knitters are the long-tail cast-on and—for additional stitches needed for sections like sleeves—the backwards loop cast-on.
But there are many, many more cast-ons out there in the world, and in fact, there are many books and resources about them. In a December episode of YarnCraft (the Lion Brand podcast that I co-host), we talk about many of the different ways to cast on and bind off your project.
I often use a new project as an opportunity to practice a new skill. In the past, I've practiced the Old Norwegian Cast-On while making a cowl as a gift—I chose it because it's extra stretchy, perfect for a cowl being slipped over the head. Currently, I'm working on a new project, and I decided to try Judy's Magic Cast-On, pictured right (often used for seamless sock-toes, but in my case, I'm using it to create a seamless bottom to a tote bag knit in the round).
I love that even after years of knitting and crocheting, I can still learn new skills to add to my repertoire. Each new cast-on serves a different purpose and will give you a new way of looking at the beginning of your project.