Cosmological scenarios with $k$-essence are invoked in order to explain the observed late-time acceleration of the Universe. These scenarios avoid the need for fine-tuned initial conditions (the ``coincidence problem'') because of the attractorlike dynamics of the $k$-essence field $\ensuremath{\phi}$. It was recently shown that all $k$-essence scenarios with Lagrangians $p=L(X){\ensuremath{\phi}}^{\ensuremath{-}2}$, where $X\ensuremath{\equiv}\frac{1}{2}{\ensuremath{\phi}}_{,\ensuremath{\mu}}{\ensuremath{\phi}}^{,\ensuremath{\mu}}$, necessarily involve an epoch where perturbations of $\ensuremath{\phi}$ propagate faster than light (the ``no-go theorem''). We carry out a comprehensive study of attractorlike cosmological solutions (``trackers'') involving a $k$-essence scalar field $\ensuremath{\phi}$ and another matter component. The result of this study is a complete classification of $k$-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form $p=K(\ensuremath{\phi})L(X)$. Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous ``no-go theorem'' still holds for this class of models, indicating the existence of a superluminal epoch. In the context of $k$-essence cosmology, the superluminal epoch does not lead to causality violations. We discuss the implications of superluminal signal propagation for possible causality violations in Lorentz-invariant field theories.