I am new to programming and am wondering what area I would enjoy the most. So my question is what general areas of programming are there?

That's only somethin you can determine for yourself. Personally, I enjoy writing enterprise apps. Probably that's because it's what I get paid for :)

There are a lot of different areas. Network programming, web applications, embedded systems, 3d apps, etc. If you don't have any programming experience, you should just start learning a language and figure out how to use it well. From there you can expand to specific areas of programming. You have to have a solid grounding in the basics first.

You can do what you like, if you like games, well so 3d apps, if you like web-design. It depends of your like's. But if you really get into it, automatically you will be learning other things. For example i started with HTML, then PHP, then SQL, ASP

There are 2 directions as I think - basic software developing, like building a house on my fished from needed materials, and solving some specific problems (algorythms). And you can choose what you like more