The "compose" key on Linux is one of my favorite things about the Linux keyboard system. You can pick which key is your "compose" key, choosing from about a dozen options. Then just as you describe, you type it in sequence (though on Linux, compose then c then s produces š, because compose then c is the shorthand for the "caron" diacritic: compose, c, g is ǧ, compose, c, h is ȟ, and so on).