The few things you have to look out for when swapping V8 engines into a II compared to other Fords:
The flywheels/flex plates and the corresponding clutches/torque converters are smaller diameter requiring a smaller bell housing that was engineered for the II. Standard bells can work with modification.
II oil pans are specific to IIs. Other front sump pans are usually too deep and interfere with the rack and pinion causing issues when bolting the motor mounts. This is the main reason swapping a 351W is such a PITA.
Motor mounts, both frame side and engine side, are unique to the II. IIRC, the engine is offset in the engine compartment by about 2 inches. I could be wrong on the amount, but I know that they are offset. If memory serves, the passenger side frame mount is the same for all IIs, it's the driver side that's different. I could be wrong again, but I swapped one car from a 4 to a 302 and the passenger side seemed to be correct, but it's been a long time.
Exhaust manifolds are II specific for the confines of the engine compartment. I honestly don't know if any other manifolds will work or not. It's my understanding that they do not.
To go along with the smaller ring gear on the flywheel/flex plate, some people have reported that IIs require a specific starter. I have yet to run into a problem. Maybe I'm just lucky?
That's about all I can think of off the top of my head. Any 302 can be made to work if you can work around these issues, so I don't think you made a bad purchase. And welcome to Stangnet from a former Iowan!