Can't really help you decide between the 200t better or nx200t Fsport but it shouldn't vibrate at start up. The one other mention of vibration on the forum is when someone was accelerating between 45 to 65 and it could have been caused by the axle. Here's the relevant thread: http://www.lexusnxforum.com/forum/153-nx-issues-problems/4665-nx200t-vibration.html
Did you mention this to the salesperson while test driving the car?
Did you mention this to the salesperson while test driving the car?