Apart from other excellent suggestions:

 - *3264 and all that*, David Eisenbud and Joe Harris.

Contains a wealth of useful information, such as a glimpse of intersection theory, geometry of Grassmanians, Chern classes, Hilbert schemes and a toolbox for Riemann-Roch.

 - *Lectures on Vector Bundles*, J.Le Potier.

Concise introduction into Quot-shemes, moduli spaces of sheaves and stability conditions.

 - *The Geometry of Moduli Spaces of Sheaves*, D. Huybrechts and M. Lehn

Another (more thorough) treatment of semistable coherent sheaves.