In this paper, we present a study of basic classes of stationary observers orbiting in stationary and axially symmetric Kerr-de Sitter spacetimes. Along with proper definitions of these classes, we focus on their possible matching on particular circular orbits. Especially, we determine a number of such orbits in a given spacetime characterized by its rotational and cosmological parameters that leads to a comprehensive classification of the Kerr-de Sitter spacetimes. Studied profiles of orbital velocities of the observers and of forces keeping them on their orbits directly reflect complex structure of the Kerr-de Sitter spacetimes that is caused by a unique interplay of attraction and rotation of a central object and an ambient cosmic repulsion.