I’m not sure the direction is that important, but I always use three fingers to represent the Trinity. (There was a big dispute a couple of centuries ago about the number of fingers among the various Orthodox in Russia - all of them a little too tightly wrapped, IMHO!)
I think the American style can be a little sloppy. Latin Americans and many Europeans tend to cross themselves with one or three fingers and kiss their fingers afterwards. I often make a tiny sign of the cross with my thumb on my chest when a regular one would be impossible or ostentatious.
That said, I don’t think it’s that important. But it should be careful and respectful, unless you’re at the point of death...in which case, cross your arms.
My mother taught me to use my forefinger and my middle finger, and the sisters in school taught me the same way. I can’t be the only one here who learned that way.