Java is not a complex language, altough it looks frightening at first.
I started learning Java from home, not a school, at 15 years of age (yes, yes, I know that's nothing to brag about) trough a book. It's a norwegian book, so I won't link to amazon;)
After reading/hacking trough half the book I found out I was better off ditching the book and looking for more stuff online. Google really IS awesome!
I would often read about all the fancy features of the JVM, frameworks, third-party libraries, JSRs and so on, and how much better my life would be with them all, but I just ignored them all. Yes I tried, but found it too confusing to learn Java and a framework that wasn't really necessary, at the same time.
Some people gave me hell for not using insertRandomLibraryName() or insertFancyFrameworkName(), and told me all about how much time and effort i would save, but I'm glad I didn't listen.
Now times have changed, and I still learn new things, or easier ways to do old things, every day. And I'm glad I took the time to learn the language itself before all the fancy stuff.
Also, don't use a notepad for writing code, use an IDE from the beginning. The only one I've ever really used is NetBeans, so that's the only thing I can recommend, but I sure am really happy with it!
As to Java SE, ME and EE, start with SE, and you'll propably find that it's enough for now. You don't have to use EE to write for the web, SE is fully capable of webernet stuff;D