Also here is a tutorial I have used and it is great for starting out in SFML. It shows you how you can set up SFML and any other library in Visual Studios C++. It also shows you how to make a pong game with SFML.
"Since Q1 2007, binary version of PhysX SDK is free for commercial and non-commercial use." - source Better read the license though, just in case (and I can't seem to find the actual license anywhere, so you probably need to download it to find out for sure).
You could also try Bullet, which is open source. (zlib)
OpenAL = Open source sound, if you use an earlier version. Later versions are proprietary, according to wikipedia. (Then why's it called "Open"?!) Networking = Berkley sockets, but that's rather low level. ENET maybe? RakNet is higher level but is a commercial product.
Torque 3d has good networking and you can add ai bots. But I prefer UDK, it is really really easy to add ai and you can make ctf, tdm, or ffa game in a few minutes. If you have any other questions about udk, please ask.