The obvious choice for Charlie chinos, is chino fabric, which is a cotton twill fabric. These days it's often sold as a blend to a little bit of stretch, which is optional.
But you have a lot of options here, and your choice of fabric will influence what sort of style these project.
Go for wool for the most classic look. Check the suiting section of your fabric store for options. If this is your first pair, some wool-poly blend is most likely going to be more budget-friendly. But don't let price alone guide you, buying some cheap whimsical fabric is the best way to come up with a shitty looking pair of trousers, and get frustrated in the process.
For cotton, go for a heavier weight. Cotton might also be a bit easier on the beginner than wool. If unsure what to use, ask for chino in the fabric store and simply pick a colour you like.
Nothing beats linen on a hot summer day. It's fun to work with too, but it does wrinkle like a mofo, and even the most neatly made trousers look somewhat messy when made in linen. What I'm saying is, maybe not for your first pair.