Advice Pleas on rear end.

Advice Pleas on rear end.

Ok first some info on the car I have. It a 1966 Plymouth barracuda that one of the previous owners has put in a 318 with 360 heads and edelbrock 316-360 intake with a 600cfm carburetor.

I had to take apart the top end and replace all the gaskets and rebuild the carburetor. It’s all back together now and runs ok. When you get to about 45-50 MPH you get a roar out of the rear end so I’m sure I need to go thru it 100% and replace all the carrier bearings.
My plans for this car are to have a good driver with a strong motor and drive train. The game plan is to put SB 360 with a 727 transmission in this car.
My question is should I just rebuild the rear end that is in the car or should I start fresh and if so what should I be looking for and what would work best with my setup.

Thank you for your time.

Will