We present ISO photometric and spectroscopic observations of a sample of 57 bright Asymptotic Giant Branch stars and red supergiants in the Large Magellanic Cloud, selected on the basis of IRAS colours indicative of high mass-loss rates. PHOT-P and PHOT-C photometry at 12, 25 and 60 $mu$m and CAM photometry at 12 $mu$m are used in combination with quasi-simultaneous ground-based near-IR photometry to construct colour-colour diagrams for all stars in our sample. PHOT-S and CAM-CVF spectra in the 3 to 14 $mu$m region are presented for 23 stars. From the colour-colour diagrams and the spectra, we establish the chemical types of the dust around 49 stars in this sample. Many stars have carbon-rich dust. The most luminous carbon star in the Magellanic Clouds has also a (minor) oxygen-rich component. OH/IR stars have silicate absorption with emission wings. The unique dataset presented here allows a detailed study of a representative sample of thermal-pulsing AGB stars with well-determined luminosities.