In your second variation, why should w play 4 while his two stones are being in atari?
Your first variation was almost perfect, only your move 3 should be at a different position --> there is an alternative way of starting a ladder with the D15/D16 in another direction. Give it another try!
BTW - up to this stage, I like blacks position very much. White only has some few points at top side (and the ladder makes it even worse), while black is more or less present on the whole board. Thus, your opening was already quite well played.
Now its ladders, nets and other important fighting stuff to focus on. You may want to have a look at http://senseis.xmp.net/?LessonsInTheFundamentalsOfGo and (after some practice) http://senseis.xmp.net/?LadderProblemsAndExercises.
Edit: I added the ladder after move 19 in my review