We used Spitzer's Infrared Spectrograph (IRS) to observe stars in the Small Magellanic Cloud (SMC) selected from the Midcourse Space Experiment (MSX) Point Source Catalog. We concentrate on the dust properties of oxygen-rich evolved stars, which show less alumina than Galactic stars. This difference may arise from the SMC's lower metallicity, but it could be a selection effect: the SMC sample includes more stars which are brighter and thus more massive. The distribution of SMC stars along the silicate sequence looks more like that of Galactic red supergiants than asymptotic giant branch stars (AGBs). While many are definitively AGBs, several SMC stars show evidence of hot bottom burning. Other sources show mixed chemistry (oxygen-rich and carbon-rich features), including supergiants with PAH emission. MSX SMC 134 may be the first confirmed silicate/carbon star in the SMC, and MSX SMC 049 is a post-AGB candidate. MSX SMC 145, previously a candidate OH/IR star, is actually an AGB star with a background galaxy at z=0.16 along the same line-of-sight. We consider the overall characteristics of all the MSX sources, the most infrared-bright objects in the SMC, in light of Spitzer's higher sensitivity and resolution, and compare them with the object types expected from the original selection criteria. This population represents what will be seen in more distant galaxies by the James Webb Space Telescope (JWST). Color-color diagrams using the IRS spectra and JWST mid-infrared filters show how one can separate evolved stars from young stellar objects (YSOs) and distinguish among different YSO classes.