My first impression is a U-joint but this is a transs-axle car. I am hoping that the free play and vibration is easily repaired and not internal to the transmission. Please respond only if you have actual similar experience and a positive resolution.

 

When shifting, do you mean shifting from Park to Drive, or do you mean when you are already in Drive the car is clunking before shifting?

I would check all engine/trans mounts first. That's the easy part.

If it's a clunk and vibration when taking off from a stop, then it could be transmission related if it's not a mount problem.

 

Yes, clunk is when shifting from park to either drive or reverse

 

You have only given really limited information here?
But I had a front wheel drive car that had this issue 3800 motor about a 100K plus miles my shop changed the trans fluid and it went away.
The vibration issue can be in the wheels and tires, if you over torque the lugs when you put them on, it will cause a vibration.
If the tires have an issue this may cause a vibration.
Alignment is something to check also.

 

Then I would start with the engine mounts. When you shift from park the engine will rock.

It's pretty common for those mounts to collapse on themselves.

 

OK what about CV joints

 

CV Joint would be more of a vibration and a noise while turning, as opposed to a clunk during the shift out of park.

 

yes my car did that, ended up the rubber bushings in the front dog bone mounts were wore out, east cheap fix.