1500USD to build as much horse in a 360 as possible. What would you do?

I really think you will have more money into it than $1500US but you must begin somewhere. I agree with Moper and others, on such a limited budget, I would keep it pretty simple:

The bottom end would be rebuilt using a quality rebuild kit using moly rings, and possibly KB107 pistons. The heads would also just get a stock type rebuild with a 3 angle valve job and a basic port clean up.

Cam wise, a Comp XE262 or XE268, depending on your exhaust system. Comp does a "K kit" which comes with lifters, chain, springs and such.

Edelbrock Performer RPM (non-air gap) intake and an Edelbrock 1406 or 1407 carb, again depending on your exhaust system.

If this engine will be installed into a 66 or earlier A body, the exhaust system will be your biggest challenge. You could quite easily spend your entire budget on the exhaust. As you have noticed, headers which do not require cutting the fenderwells out are quite expensive for this car. If you plan on racing or building a more powerful engine in the future, buy the Hooker Super Comps and start cutting. If you plan to use the original cast iron exhaust manifolds, the XE262 cam and 1406 carb would be a better choice. No point in a 6000 RPM cam with 4000 RPM manifolds.

A totally stock 360 with the XE262 cam and 1406 carb will move 66 Dart around quite well. It will certainly have enough power to destroy the original rear axle.

Also, to balance an "externally balanced" engine, the crank damper, and torque converter must be spun with the crank, as they are part of the counterweight system.