Word / Code Completion in VIM

Question

I know that I can get word completion through CTRL+N & CTRL+P and code completion through omnifunc with CTRL+X CTRL+O. I

Answer 1

:set completeopt=longest,menu,preview

maybe?

(I'm not sure if your statement

"when I press TAB, it should do nothing, because there is no more common ground than te"

conflicts with your later statement

"to testor after a 2nd TAB."

It seems to me that there's no more common ground than "test" at that point... Unless you mean the first tab goes to the longest common ground, and then the subsequent tabs cycle through the other matches, in which case you're after what I have above...)