Transiting exoplanets provide access to data to study the mass-radius relation and internal structure of extrasolar planets. Long-period transiting planets allow insight into planetary environments similar to the Solar System where, in contrast to hot Jupiters, planets are not constantly exposed to the intense radiation of their parent stars. Observations of secondary eclipses additionally permit studies of exoplanet temperatures and large-scale exo-atmospheric properties. We show how transit and eclipse probabilities are related to planet-star system geometries, particularly for long-period, eccentric orbits. The resulting target selection and observational strategies represent the principal ingredients of our photometric survey of known radial-velocity planets with the aim of detecting transit signatures (TERMS).