  We use constructions of surfaces as abelian covers to write down exceptional
collections of line bundles of maximal length for every surface $X$ in certain
families of surfaces of general type with $p_g=0$ and $K_X^2=3,4,5,6,8$. We
also compute the algebra of derived endomorphisms for an appropriately chosen
exceptional collection, and the Hochschild cohomology of the corresponding
quasiphantom category. As a consequence, we see that the subcategory generated
by the exceptional collection does not vary in the family of surfaces. Finally,
we describe the semigroup of effective divisors on each surface, answering a
question of Alexeev.
