Casting on stitches is genuinely the key moment, because everything depends on it. The most comfortable and reliable method is the German cast-on (or two-needle cast-on). The idea is simple: you take the yarn with a bit of extra length (roughly three times longer than your future row), make a loop on your fingers, and then insert the needles into that loop so you catch the working yarn from one side and the long end from the other. You get a strong stitch that doesn't unravel and doesn't pinch the needle.
The main thing is not to pull the stitches on the needle too tight. After each cast-on stitch, slowly slide the stitches toward the needle tip, but leave a little gap between them. If you tension the yarn too much while casting on, you won't be able to work the first row afterward. Try to relax your hands and work more slowly - the stitches will naturally ease up from the excess tension over time.
One more tip: if the stitches keep unraveling while you're working, it means they were cast on too loosely. Try casting on a bit tighter next time, but not so tight it hurts your fingers. Ideally, the needle should slide into the stitch easily, and the stitch itself should sit securely on the needle without slipping off.