Never watched anime, will I like this one for a start?

Yes, I think it's completely possible to enjoy this even if you've never watched anime. I have friends who aren't really into anime and they've enjoyed this.

As for the plot -- and without giving too much away -- it's about a highly intelligent young man who comes across a seemingly ordinary notebook. He soon finds out that this notebook is connected to something supernatural, and that if you write a name within its pages, that person will die. It's incredibly quick and suspenseful in its pacing, which makes it very fun to watch. It does, however, suffer from a drop in quality after the loss of one of its characters.

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'Save me, Barry!'

Yes, this is EXCELLENT for a start. Dragon Ball/Dragon Ball Z, Cowboy Bebop, and Yu Yu Hakusho are other ones that anyone can enjoy regardless if they're into anime or not. Most animes are somewhat of an acquired taste but these are easily accessible.

I've never been much into anime myself, but I was hooked on this show instantly. I loved it, and it's now one of my favorite TV shows ever. And actually it's partly because of that that i've been getting into more anime lately (though the main reason is i'm studying Japanese and need exposure to the language).

The people, and the people alone, are the motive force in the making of history.
-Mao Zedong

The problem with this one is that if you like it as much as most people you will wander the earth for the rest of your life looking for another one that is as good.