2002 Chevy Cavalier Shifting Hard
 

I bought my car brand new June 2002. I've been pretty much the only driver. It has a little under 151,000 miles on it. It has been shifting hard alot while driving it, especially when starting after a stop sign or traffic light or picking up speed. It seems to be idling hard as well. When I first start it without putting it into Drive, the rpm needle bounces from 0 to 1. You can feel the steering wheel vibrating. I just spent $400 to have the water pump replaced and left tail light switch fixed. It also stalls out several times a day, when I'm at a light or stop sign. Also stalls if car is off, I turn it on & put it in drive. The garage told me eventually my transmission would go. I think there is some other underlying issue. Plus my check engine, light is on, sometimes no traction comes on.out of the blue & check gages for gas comes on & I have alot of gas left. Any input you can provide would be wonderful. The garage just checked to see if I had transmission oil and if it was leaking, it wasn't. Should I take it to Auto Zone to have the codes run & printed out first to try & pinpoint the problem?