I'm with JJR on this one. I'm confused about whether you have a manual or an auto. If you have an auto, it really is bad practice to shift into neutral all the time, and I wouldn't be surprised if it accelerated the demise of your transmission. If you have a manual, then good for you. It is smart to pull the car into neutral when coming to or at a stop. This relieves the throw out bearing from doing unnecessary work.
As for your noise/jerk, jack up the rear of your car and inspect items in this order; (1) Rear differential bushing (2) Driveshaft guibo/flexdisc. Report back. If either of these items get bad enough. They can turn a slight bump into a loud thud or jerk. It all depends on their condition. Sure it could be your trans, but why start there when it takes maybe 10 minutes to check these items?