Whoops, I saw this earlier and finally found it again. C3 and C4 are designations for Ford automatic transmissions. The C3 didn't show up until the late '70's or early '80's.
For a 289/302V8 'Stang:
If you're 3 spd is working and you don't plan on drag racing you can keep it in but is it's shot...
The 4 speed should bolt right in with the same engine mount. If you have a '65 (not sure for other years) you may have to change the trans yoke to the 4 spd type and this may mean a different drive shaft as well. I had a '65 V8 3 spd and when I converted it to a C4 auto trans the drive shaft yoke didn't fit and I think they were different in length. On the other hand, on my previous '65 FB I swapped the same C4 with a 4 spd top loader and the trans yoke and drive shaft fit (drive shaft may have been a bit long, though).
If you have a '65-'66 six cylinder then you have major work. The '65/'66 three speeds used a different bell housing from the Dagenham 4 speed. A better route would be to grab a manual trans bell housing from a '67 and up I6 and use a toploader 4 spd. You still may run into trans yoke/drive shaft issues.