We analyze Hubble Space Telescope images of a complete sample of 341 galaxies drawn from the CFRS and LDSS ground-based redshift surveys. In this, the first paper in the series, each galaxy has been morphologically classified according to a scheme similar to that developed for the Medium Deep Survey. We discuss the reproducibility of these classifications and quantify possible biases that may arise from various redshift-dependent effects. We then discuss automated classifications of the sample and conclude, from several tests, that we can expect an apparent migration with redshift to later Hubble types that corresponds to a misclassification in our adopted machine classification system of ~24% ± 11 of the true "spirals" as "peculiars" at a redshift z 0.9. After allowing for such biases, the redshift distribution for normal spirals, together with their luminosity function derived as a function of redshift, indicates approximately 1 mag of luminosity evolution in BAB by z 1. The elliptical sample is too small for precise evolutionary constraints. However, we find a substantial increase in the proportion of galaxies with irregular morphology at large redshift from 9% ± 3% for 0.3 ≤ z ≤ 0.5 to 32% ± 12% for 0.7 ≤ z ≤ 0.9. These galaxies also appear to be the dominant cause of the rapid rise with redshift in the blue luminosity density identified in the redshift surveys. Although galaxies with irregular morphology may well comprise a mixture of different physical systems and might not correspond to present-day irregulars, it is clear that the apparently declining abundance and luminosities of our distant "irregulars" holds an important key to understanding recent evolution in the star formation history of normal galaxies.