I have the same car as you, also planning to go the 360 route, although the 318 is easier to find parts for. I'm going to swap in a 4-speed, but the cost to fix the "good" 4 -speed trany I bought was way more than just buying it. It turned over good, shifted into all gears, but I always tear down everything for inspection. The result: a piece of sh... that needed $$ to fix.
With some help, you could build the engine yourself and have fun doing it, or be real careful and find a shop with great references.
I used to have a 340 duster with auto trany, thermoquad carb, OEM disc/drum brakes and factory electronic ignition. Ran the crap out of it for 130,000 miles. That 727 is a tough trany, and I've heard good about the 904 with the right parts. Sold the duster to an oil rig worker headed for Alaska. Saw him years later, he said everywhere the duster went was at 100 mph, finally cracked the frame apart pounding the alcan highway.
So in conclusion, IMHO, factory disc drum brakes would be fine, even 318's can be built to go fast if your on a budget.
I don't have the deep pockets either, like lots of folks around seem to have. I will admit the cost of going thru a Challenger is more than expected. Its like building a house. You better look at the expenses every week or its easy to far exceed the budget.