73/74 or 93/94? You have 7x in the topic title and 9x in the topic itself. If you have a photo we can identify it for you!
If it's a 73/74 2 door it could be a KE20 or a KE25, where KE25 is the coupe version.
Ke20's (in Australia) are also 2 door, but have a shorter back end. Here are some links
to good examples of each car.
KE20 - RA28GT's KE20 Corolla
KE25 - Queen20V's KE25 Corolla
As for turbo motors, there aren't many that will drop straight in with little or no modification. 4age's or 4agze's are a popular conversion
with all KE Corolla's, but are not a turbo motor. CA18DET and SR20DET are probably the next most popular motors to be put into these cars.
After that, Rotary motors would be the next most popular motors for turbo conversions. All of which do require a certain amount of modifications
and upgrades to complete the conversion.