I have been dreaming up a fandom for the past few months. Note: dreaming up, not writing down. I just don't ethically support writing fanfictions. However, I am hooked on this story for the elements in it which have nothing to do with the original writer's trademark, things like flaming youth and broken spirits, and I know I have to write something down.
  In fact, this story has given rise to something original, but I'm in danger of crowding out my own work with the other person's. I suppose even fear plays a role in hindering me.
  Any suggestions on how to stay focused on my real story, without bringing unnecessary and unoriginal elements into it? And how not to be scared to death of doing so?

unfortunately i have never been in that particular position, never having written any fanfics. however! try just writing down whatever, and then have someone read it. have them tell you if it reminds them of the book that inspired you. if it does, revise like crazy and try again. ((oh well.)) if it doesn't... well then you're in luck! ^_^

Can I ask what it nearly is a fanfic of?

I know the feeling, but for some fandoms... for the creator, there is nothing ethically wrong with fanfics. Hell, there are people who make and sell doujinshi (in Japan) with the blessing of their creators - every doujin or fanfic brings recognition to the original.

What is it a fanfic of, if I may ask? Is it something you can skate around carefully? After all, there's no such thing as an 'original idea': most everything's been done before in some way.

  Dragonball Z (is girlier and has deeper character development than the original, without deviating from what is shown).
  That's another thing. Akira Toriyama lets people make DBZ movies that don't fit into his story at all, so I wonder if he'd really be opposed to a fanfiction.
  But I don't see how I could sell a fanfiction, and I'd rather use the non-trademarked ideas for something totally original.

The fact that DBZ doesn't have that much depth in their character creation really works for you.

In my viewpoint, the problem comes if you assume your readers should know the plot of the manga, in which case you're burning the "fanfic"-brand on the story. If you have a way of explaining the history (possibly in a creative, original way), you could breach away a little.

How about names? Are you using Toriyama's names for the DBZ character's and places?

I generally steer clear of fan fic too. I think I wrote some for Dragon Lance back in high school, but I also don't remember it being very good either. I suppose the most important thing is to make sure you stay true to yourself and make the story your own, but when you're working that closely off of someone else's work it's a very fine line to tread.

No such thing as an original idea maybe but there is such a thing as copy right infringement and trademark restriction, to say nothing of protected intellectual property, like I said; A very fine line to tread...

Well yeah, but the copyright infringement is a really, really thin line.

For instance... Group of people travelling somewhere to fight something that's bringing destruction to the world - Gensoumaden Saiyuki.

How many times has that been done before? Hell, that was my first NaNo project (farm boy, farm hand, younger sister and undead priestess going to fight person killing off the world), and I hadn't even read Saiyuki then. It's even the basic premise of Steven Erikson's books, although he's got rather more characters and they get really confusing after a time.

It is a very thin line, but it's also one you get past by not actually using any place names, character names of dialogue. There's little people can do about 'inspired by', that's how TV movies get to completely butcher up their version of newsworthy events. ;) They only ever get into trouble for it if they write something that concretely states their inspiration.

I mean, the amount of manga I've seen that is just like every other manga out there. After all, Kare First Love's been published, with characters that look near exactly like Kare Kano's and no doubt a plot near exactly the same - downside with highschool romance dramas, really: they're pretty generic.

Even one of the most original manga I own - Ray, a story about a girl with X-ray eyes - is unoriginal in its premise: the girl was created so people who needed skin grafts or had accidents or problems that required something like a new heart, lung or leg could simply take the body parts from the children in the unit. This has also been done in Michael Marshall Smith's novel 'Spares', a short story also of his, and the movie The Island (which was actually rather derivative of Spares, even down to escaping clones, yet I combed the credits and Marshall Smith wasn't credited at all - and since the character that escaped in his short story - the precurser to his novel, in fact - never actually MET the person he was a clone of, they had no need to credit it, even if it was nearly exactly the same story in places).

So like I said, it depends mostly on people using names, places and dialogue. Skirt enough around it, and no matter how blatantly it might be referenced, nothing can be done...

Shame though, since Marshall Smith's book and short story are great, and he could use more readers...

  Since it is still in the fandom stage, yes, except for characters I created. I also have had to create the cultures of some aliens, since Toriyama doesn't go very deep with some of the ones I'm using.