Hmm, this is a puzzler. If the temp gauge on your dash really is going up, it's hot hot hot. 3/4 of the way up is around 230-240 degrees.
So this is what we know:
1. New radiator (autozone radiators are fine, I've used them)
2. New water pump
3. New thermostat
4. Motor rebuild (overheated before rebuild)
5. Fan clutch appears fine
You've changed the 3 main components of the cooling system. It's a very simple system where the water pump circulates fluid and the thermostat controls the flow. Radiator cools the fluid. So at this point the most likely causes would be lack of pressure allowing the coolant to boil, or a failed "bad out of the box" part. Most part stores will have a coolant system pressure test kit you can borrow for free, I would start there and see if it holds pressure. If it doesn't you'll either see a leak or hear hissing noises.
A brand new OEM radiator cap wouldn't hurt at this point. If you need your vehicle to drive ASAP, you can swap thermostats with a 170 degree or 180 degree thermostat instead of the stock 190. It won't keep it from overheating but will help it cool down quicker once you get up to speed.