The biggest advantage you'll see in connecting either wired or wirelessly to your base station is that the base station performs something called "Network Address Translation," or NAT, which helps protect and hide the LAN side of your network. However, since you have the base station behind a router already, that's not necessary anyway, since the router does the same thing.
In fact, , unless you have your base station set to bridge, it may be that any connection-based problems you're having with your PC are caused by trying to go through two different stages of NAT-which will confuse the begeebers out of just about any net-based software.
Unless you really want to lounge on the sofa while using your Mac, you can plug it into the ROUTER and all will be well. On the other hand, you can get all of your wireless stuff working well by setting your base station up to bridge between the wired and wireless parts of your network. Go to the Network tab in the AirPort Admin Utility, and uncheck the "share a single IP address" box. Once that's done, your base station will simply act like an extension of the LAN that your router manages.
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