Under pressure, writing legibly, I can churn out "the quick brown fox jumps swiftly over the lazy dog" in about 10-12 seconds using a combination of print and cursive, and 14 seconds using just cursive. I've only started writing using cursive lately, though.
So that's anywhere from 50-60 wpm using a mixture of cursive and print, and just over 40 using just cursive. That is, if I write legibly (the cursive is less pretty, but still legible).
I'm not sure what would be the fastest method, it differs from person to person. You'll get some people saying that cursive is faster, some will say a mix is faster and some will say that printing is faster. I would just try to improve what you have right now, to start off with, unless you are interested in learning cursive.
The most popular and commonly suggested hand would be Palmer's Business Writing, there is a link stickied at the top of this forum. It's a nice simple and clean cursive form, very legible and pleasing to look at.
I'm not sure...copperplate is the way to go for speed, though. Regardless, you should post up a sample of your handwriting, it may help people answer your questions.
I have recently posted a ton of samples of my handwriting in about every thread,and I'm starting to feel bad about how much I'm flooding these forums with all my stuff, regardless, here you go.
This is my reasonably quick writing, I wrote it a few days ago, and since then I have been working on slant consistancy ( to very little avail). I know I am risking insulting somebody, but with my very untrained eye, my handwriting looks like a laughable attempt at italic I think? I don't really know, I would be tickled pink if somebody could actually recognise the style my handwriting actually is!