I'm not an author, but I often wonder if I was to write a novel would it be best in third person or first person? I like being able to delve into the main character's thoughts in first person, but I also like the "all knowing" omniscient view that comes with third person. Is there a style of writing that could allow for both of these aspects?
Third person limited may be what you are looking for. This is where the narration is given in the third person, using third person pronouns, but is limited to the thoughts and experiences of one character.
This style allows you to see inside the head of a character, but it isn't quite as limiting as first person. For example, you can write a scene from the point of view of another character, and if you do it right, it won't be too jarring for the reader (this is sometimes called third person alternating). This allows you to give away important information that the main character doesn't know.
The Wikipedia page on narration explains various narrative perspectives and some examples of each.
Third person is the best way to go, especially if you are a novice writer.
Many writers make the mistake of using first person narrative thinking they need to explain what's going on instead of showing what's going on.
While I write plays, they follow the third person even though every character is speaking in first person. But it is the character speaking, and not the writer telling.
If you are very skilled, you could get away with a first person narrative, whether injected into a story or do a whole story in first person.
You need to be a skilled writer to pull that off. It is not that it is difficult to write. What is difficult is to get your readers to buy into it. That is where the skill resides.
In plays, I have to use diaglog that advances my plot, and if I write in an action scene, it must also do the same. Most plays, it's not about the dialog as much as what is done on stage with it.
I strongly prefer third-person limited in much of my own writing, but there are few cases where first-person stands out:
- when your viewpoint character has a distinctive voice (e.g. Huckleberry Finn);
- when you want to have an unreliable narrator (e.g. Holden Caulfield).
There are, of course, exceptions that define the rules. The Thirteenth Tale, includes a deceptive narrator telling her history to the viewpoint character.
From what I've read, you will find a lot of omniscient-view third person in older books, but it seems to have faded in popularity. The only times I've really noticed it myself, though, it had distracted me from the story, so examples of well-written omniscient perspective could have slipped by me.
Your market might also influence the choice of viewpoint. It appears  that teen/YA SF stories these days favor first person, while adult SF favors third-person limited. I can't speak for other genres.
Use third person. As explained in another answer, third person limited is probably what you want.
Think of it this way: You are like a journalist who follows a particular character around. You see what (s)he sees. You know what he knows, because you can ask a question (off-text) and be told the answer. You know what he is thinking, because later he will tell you about it. But you don't know what anyone else is thinking because your main character does not know that. However, if your main character can decide that someone else is truthful or lying based on other things (such as a tone of voice, or facial expression), you can report that. You can also report what your main character would easily be able to discover.
So, if your main character is George, you can write, "Sally was born in Illinois," because George could learn that, and tell you. But you could not write, "Unknown to George, Sally..." because George would not know.
As I see it, the sole advantage to first person is that you can exaggerate or lie. You are speaking, not narrating. Thus: "I walked into the bar, which stank like my old gym shoes. The barmaid looked like an old girfriend. The liquor tasted like cheap generic booze diluted with horse piss. Etc." None of that is true. A Third-person narrator would not write it. But anyone can say it, and thus a first-person narrator can write it.
Proof: Read the novels by Raymond Chandler.