clunk from rear end when engaging first gear.

Thats the sound of ford screwing you over with a crappy tranny.. Read the sticky thread related to the T-3650 and tell me if thats what you are hearing

EDIT: whoops, didnt see the year of your car.. IDK if you have the 3650 or not.. sry
 
Actually 90% of the new 99-04 Mustangs have a little slack in the driveline.

The transmission has nothing to do with it I have heard the same " slack " noise in everything from 1999 GT's to 2004 Cobra's.
 
mine did the same thing. I checked the u-joints on the ds and they where all fine. ended up being the 4 bolts conecting the ds to the pinion on the on the rearend were loose. quick turn of the wrench and problem fixed.