Routers are definitely needed in most situations. A WAP is just an added feature of the router so that you don't have to get your ethernet cables out.
Most routers have setup programs which I think are mostly crap if you have any situation that is outside of the box. The good news is that you can set up a router directly and with much more granularity by using a web browser, while wired to the router using an ethernet cable.
Look at your documentation, but usually it goes something like this. Open IE or Firefox and type in
http://192.168.0.1 (you will need to get this IP address from your docs)
Then enter user name and password (the defaults that you will also get from your docs)
Then you can usually set up your WAN connection as automatic (DHCP). And, while any IP address not on your subnet will attempt to go out the WAN connection, it really won't be going anywhere. You essentially have a closed system (except for when you enable wireless functionality and then you will want to use security).
This stuff is pretty easy once you get in and look around.