I have a 95 Camaro as well with the same problem. My problem was that my cam was eating up my lifters, and then they tried to fix the problem, and adjusted the valves wrong -- thus causing the thumping noise.
AnswerIf you hear it when first pulling out or turning from a stop, it could be loose or damaged motor mounts.Bass
The frist thing I would check would be the engine mounts.
Maybe that thumping noise is the sound of another car smashing into the rear of your car.
Bad tire? Rotate and see if thumping changes
if it was like my 99, then a belt was worn out, and will cause a chirping noise, if it is in the engine compartment, it is very likely to be a belt
Need new lifters
worn torsen differential
most likely you have a loose bearing.
Have that tire checked sometimes the belts inside can break and cause a thumping noise
water/friction
Where is the clicking coming from? Within the engine compartment or inside the car?
On our California model it is a smog device...