We present new optical spectroscopy for 342 R<18 galaxies in the Shapley Supercluster obtained with the AAOmega facility at the Anglo-Australian Telescope. We describe the observations and measurements of central velocity dispersion, emission line equivalent widths and absorption line indices. The distinguishing characteristic of the survey is its coverage of a very wide baseline in velocity dispersion (30-300 km/s), while achieving high signal-to-noise ratio throughout (median 60 per Ang). Significant emission at H-alpha was detected in ~20 per cent of red-sequence Shapley members. Using line-ratio diagnostics, we find that the emission is LINER-like at high luminosity, but driven by star-formation in low-luminosity galaxies. We use Lick indices to characterise the absorption spectra. We define a subset of galaxies with very low emission contamination, and fit the index-sigma relations for this subset. Comparing the index-sigma slopes against predictions from single-burst stellar population models, we infer the scaling relations of age, total metallicity, [Z/H], and alpha-element abundance ratio, [a/Fe]. To reproduce the observed index-sigma slopes, all three parameters must increase with increasing velocity dispersion. Specifically, we recover: Age propto sigma^0.52+/-0.10, Z/H propto sigma^0.34+/-0.07, and a/Fe propto sigma^0.23+/-0.06 (error reflects systematic effects), derived over a decade baseline in velocity dispersion. The recovered age-sigma relation is shown to be consistent with the observed evolution in the giant-to-dwarf galaxy ratio in clusters at redshifts z=0.4-0.8. A companion paper will analyse the distribution of age, [Z/H] and [a/Fe] for individual galaxies. (Abridged.)
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