A Wireless Network for a 4-Story Apt. Building?

zzzreyes asks: "I live in a 4 storey building, and pretty much everyone in this building is into gaming and computers. I have just received, through the death of a great aunt, about $7,000. I want to know how and what I should buy, to provide wireless access through out the whole building, so we can all share one connection. There are 6 double-room apartments on each side, and we only have four floors. I'll hopefully have access to the elevator shaft, in case I need it. Will $7,000 be enough?" How cheaply could you do something like this, assuming you had access to much of the building? What would be the best way to set up the access points to guarantee the best coverage for the whole building?