Infrared and electronic spectra are indispensable for understanding the structural and energetic properties of charged molecules and clusters in the gas phase. However, the presence of isomers can potentially complicate the interpretation of spectra, even if the target molecules or clusters are mass-selected beforehand. Here, we describe an instrument for spectroscopically characterizing charged molecular clusters that have been selected according to both their isomeric form and their mass-to-charge ratio. Cluster ions generated by laser ablation of a solid sample are selected according to their collision cross sections with helium buffer gas using a drift tube ion mobility spectrometer and their mass-to-charge ratio using a quadrupole mass filter. The mobility- and mass-selected target ions are introduced into a cryogenically cooled, three-dimensional quadrupole ion trap where they are thermalized through inelastic collisions with an inert buffer gas (He or He/N2 mixture). Spectra of the molecular ions are obtained by tagging them with inert atoms or molecules (Ne and N2), which are dislodged following resonant excitation of an electronic transition, or by photodissociating the cluster itself following absorption of one or more photons. An electronic spectrum is generated by monitoring the charged photofragment yield as a function of wavelength. The capacity of the instrument is illustrated with the resonance-enhanced photodissociation action spectra of carbon clusters (Cn+) and polyacetylene cations (HC2nH+) that have been selected according to the mass-to-charge ratio and collision cross section with He buffer gas and of mass-selected Au2+ and Au2Ag+ clusters.