Hey, I've been interested in Kara no Kyoukai for a while now (I mean, the movie had been released for a long span of time already), but the last time I watched it, which was only the first movie, I pretty much understood nothing.
I read a little background information, but it doesn't help that much. I pretty much have no knowledge of Type-Moon worlds or Tsukihime where it seems slightly connected. Does this mean I'll have a hard time understanding the rest of the series (of movies)?

The movies are disjointed, like the Haruhi anime. Just watch all the way through and then watch it again. You will get everything after that.

I suggest reading the light novels instead. That's not so confusing. Though only the first 4 have been translated yet. They are short, the longest of them is 40 pages (A4).
I watched the first 4 movies after reading the books, and the books were much better.

"Thus is our treaty written, thus is agreement made
Thought is the arrow of time, memory never fades
What was asked is given, the price is paid"

Search for Kara no Kyōkai on wikipedia, and you will find the chronological order of the movies. Watching them like that wil help you understand and enjoy the story more.

You dont need to read the other Type Moon stories to understand this one.

The chronological order should be movie 2, 4, 3, 1, 5, 6, 7

Super cool story.

Dont forget to watch the parts afther the credits. Some of them shows realy cute sides of the relationship between the two main characters.

Friedrich Nietzsche (1844 - 1900) - "Man is more ape than many of the apes."

Jean-Paul Sartre - "You are--your life, and nothing else."

Henrik Ibsen - "The majority is always wrong; the minority is rarely right."