what converter is right for me?

Ok everyone long story short I want to swap my 4 speed for an automatic, I was thinking with a 904 but not sure if i should use a 727. The motor I have is a mild 360 it has about 9.5 compression the car weighs about 3100 lbs, stock J heads with a strip dominator intake manifold, 750 Mighty Demon carb, the cam is a mechanical huhges cam the lift is 579 intake & 587 exhaust, duration is 256-260 @ 50". It has 4.10 gears and a 26" tall tire. It will see track time and when not on the track it will have hard street miles. Im looking for ideas on which trans to use and what specific converter would work best for my set up. Thanks for any advise I can gather.