Automatic to 360/4-speed conversion

If you want it to be "as fast as possible", I'd consider using a 904, if you go auto. Much less parasitic drag. Lots of race cars use them.

If you go stick, be careful when it comes to the flywheel, and more specifically, it's balance. I'm not sure if the 360 ever came with a stick. I think 360's were all externally balanced, and engine's that came with sticks were internally balanced. So, if using stock parts, you could end up with a bad vibration.
Maybe your 360 has been internally balanced, and maybe someone sells a flywheel that is for an externally balanced 360 if it isn't.
It's been a long time since I've considered what you're doing, so maybe someone could chime in to fill us in.

Most aftermarket flywheels (like the 440 source one for about $150) have a bolt on weight for externally balanced and take it off for neutrally or internally balanced.:coffee2: