This paper is the first in a series examining stars that were found to vary in the infrared during the course of the IRAS Sky Survey, and their application to Galactic structure studies. Here we check whether the infrared variables found by IRAS are mostly AGB stars, e.g., oxygen-rich Miras and carbon stars, as was assumed in Weinberg's recent (1992) galactic structure analysis. Our study is focused on the ''bright infrared variables'' (BIRV), a sample consisting of the 300 brightest stars in the IRAS Point Source Catalog with IRAS variability index VAR greater-than-or-equal-to 98. An analysis of optical, infrared, and microwave spectroscopy for these stars indicates that fewer than 7%, and possibly as few as 2%, are not late-type M giants or carbon or S stars. Of the 88 stars in the BIRV sample that are identified with cataloged variables, 86 can be classified as Miras. A similar analysis was carried out for a color-selected sample of stars, using the color limits employed by Habing (1988) to select AGB stars. Among the sources in this color-selected sample brighter than 44 Jy at 12 mum (the flux limit of the BIRV), 52% are classified, and of those, 38% are non-AGB stars, including H II regions, planetary nebulae, supergiants, and young stellar objects. Thus, studies using color-selected samples are subject to misinterpretation due to contamination by stars representing a wide range in properties and populations.