Hi Ben,
I program in Java at work, as well as on the MSc I'm doing part time. I couldn't recommend any book more than one called Head First Java by Kathy Sierra and Bert Bates, it takes you through the whole Object-Oriented way of programming in a pretty interesting way. Get a hold of that and a copy of Eclipse or NetBeans and just muck around for a bit!
It's probably worth just doing the command line stuff for a while before you get into the web-based stuff, as that can be a lot of extra stuff to learn (jsps, tomcat, possibly MVC etc...).
I couldn't really talk about the gaming stuff, I met someone who worked on the xbox and he was doing a lot of C and C++....if you learn how to program in one object-oriented language it's usually not a huge transition to pick up another after that (java and C# are pretty similar).
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