I would definitely suggest his two-part paper, **The Spectrum of an Equivariant Cohomology Ring.**

He develops a ton of information concerning $H_G^*(X)$, and forms the basis for much of its use in future papers.

In terms of studying group cohomology, you should also check out his short paper **Cohomology of Finite Groups and Elementary Abelian Subgroups** (by Quillen and Venkov) which establishes the celebrated result:  *If* $u\in H^*(G,\mathbb{Z}_p)$ *restricts to zero on every elementary abelian $p$-subgroup of $G$ (a finite group), then $u$ is nilpotent*.  This paper is not even two pages long, although his original proof was contained in a different paper ("A Cohomological Criterion for p-Nilpotence").