I am roughly in the same boat, but I'm not done with the engine yet (I just got the car about four months ago).
First off are your power figures. Are you running a high compression piston, or a wild cam with some monster flowing heads? Getting up to 600 on a 383 NA would typically require one of those. Most 383's end up in the mid 400's for power, but with huge torque. Anyways, I'll assume that's right for now.
A 700R4 will work, but you will need one of the better/best custom transmissions to handle that torque. Phoenix Transmissions or Pro-Built Automatics make something that will fit your needs, to the tune of $2000 or so.
For the exhaust, I would look at long-tube headers with custom dual 2.5" mandrel bent pipes. Do it right the first time, this car will need the dual system now or later.
A built 12-bolt or 9" would be highly recommended. The 10-bolt rear is good to 400hp, maybe, and that's with some beefing up. I'm on the fence as to whether I want to beef up my 10-bolt, as I won't be running slicks. You'll probably never hook up without slicks.
Just my slightly educated opinion. That's one hot looking engine, btw