The car makes a light grinding/clunking noise at.

I think I'd start by looking at the flexible coupling in the exhaust pipe near the rear of the engine, and possibly the engine mounts. One of them controls how much the engine rocks when you accelerate and change directions.

There is a tool you might be able to borrow or rent from an auto parts store that borrows them called the "Chassis Ear". It is a set of six microphones, a switch box, and headphones. You clip the microphones to suspect points, then drive around while listening with the headphones. You can move the microphones around to zero in on the source of the noise. Be aware that many mechanics have never seen or even heard of this tool. Suspension and alignment mechanics use it to find rattles, squeaks, and other noises.