It has recently been discovered that some, if not all, classical novae emit GeV gamma-rays during outburst, but the mechanisms involved in the production of gamma-rays are still not well understood. We present here a comprehensive multiwavelength data set-from radio to X-rays-for the most gamma-ray-luminous classical nova to date, V1324 Sco. Using this data set, we show that V1324 Sco is a canonical dusty FeII-type nova, with a maximum ejecta velocity of 2600km/s and an ejecta mass of a few x10^-5^M_{sun}_. There is also evidence for complex shock interactions, including a double-peaked radio light curve which shows high brightness temperatures at early times. To explore why V1324 Sco was so gamma-ray luminous, we present a model of the nova ejecta featuring strong internal shocks and find that higher gamma-ray luminosities result from higher ejecta velocities and/or mass-loss rates. Comparison of V1324 Sco with other gamma-ray-detected novae does not show clear signatures of either, and we conclude that a larger sample of similarly well-observed novae is needed to understand the origin and variation of gamma-rays in novae.