how to move cursor directly to the next new line?

This question is quite hard to understand, but i think you're either asking for how can you create a new line in command mode (use 'o') or how can you move down a line in vim ('j').

If it's neither of these things you wish to know, please say.

The simplest way is probably hit ctrl-o then $.

ctrl-o puts you into command mode for one command only, so the $ puts you to the end of the line, then you're automatically back into insert mode, and can continue your edit - i.e. hit enter an you're on the next line.