As I shared in Rylis' thread, I'm a proponent of a stock stroke 360. A basic rebuild with Eddy heads will give you more power than you need for a beginner.

If I were in your shoes, I'd stay with the iron heads and just freshen up the motor with a cam and intake. Lots of bang for the buck in J heads. If the heads require work, go with a set of out of the box edelbrocks.

K.I.S.S. It'll be cheaper, easier to maintain, more reliable, and you'll have less down time. The more exotic you go, the longer it will take to complete and swallow cubic dollars.

I built my 360 up over 3 years as I bought parts as budget/deals allowed.
Externally balanced (B&M flexplate for converter)
KB Hyperuetectic pistons
Hughes Stage 1 Eddy Heads
Hughes custom grind cam, lifters, pushrods, and rockers
Eddy Air Gap
Quick Fuel 750 Slayer (started with a 670 Avenger but it wouldn't run right)

This motor is a torque monster that Hughes helped me build for autocross. I am very happy with it. However, the Hughes top end was more than half the cost of the build and was one of those "might as wells" as I knew I wasn't going to be single much longer. I probably could have gotten 90% of where I am with more traditional components, and saved a bunch of money. However, since I needed decent heads, I still would've gotten the Edelbrock's. Just maybe not ported.