I have read most of Newstead this term. It is easy to read, barely mentioning schemes, and introducing moduli through basic examples of classifying endomorphisms of a finite-dimensional vector space. Eventually one is led to studying moduli of vector bundles of fixed rank and degree over a curve. With references to [GIT] profuse throughout the text, Newstead feels almost like a prolonged introduction to Mumford's GIT. It might not have the desired arithmetic flavour, but I would recommend it as an introduction to moduli. It may be difficult to find a copy though.