Since this is not purely group theoretical and not a complete answer, this maybe should be more of a comment, but since you mentioned simplicial complexes perhaps you should check out the following paper to get you started:
Haglund, Frédéric, and Daniel T. Wise. "Special cube complexes." Geometric and Functional Analysis 17.5 (2008): 1551-1620.
Which is concerned with the fundamental groups of certain square complexes (VH complexes whose 1-cells are divided into two classes, "horizontal" and "vertical", and the attaching maps of squares alternate v-h-v-h). For instance, they prove that any fundamental group of a compact virtually clean (clean means attaching maps are embeddings, and this implies that the group splits as a clean graph of groups, as studied in ) VH-complex is linear.
Although this isn't purely group theoretic, it is at least mostly presentation theoretic, and the result itself isn't too hard to apply if you have for instance a finitely presented group. In this case, there is often an easy algorithm to check whether such a group has a VH-subdivision. (For instance, there is an example of such a procedure outlined in my paper with Wise ). After you still have to check the virtually clean condition, which may or may not be so easy depending on what you are doing.
 Wise, Daniel T. "The residual finiteness of negatively curved polygons of finite groups." Inventiones mathematicae 149.3 (2002): 579-617.
 Polák and Wise, "A Note on VH Subdivisions", To appear.