Currently I've discovered my radiator had developed a small leak in one of the tanks that caused it to spray upwards. This has since been sealed and I've been browing for a new radiator but I've run into the following issue: Every site has radiators listed as with the engine oil cooler and without and I'm not entirely sure which radiator is appropriate for me. Is there any easy way to visually check whether or not my car has an EOC on its radiator already?

On your current radiator, look at the passenger side, those metal lines going in are transmission lines. Now look to the driver side.. any metal lines? If you have oil cooler they should be on the driver side.

If I am not mistaken, only the SSE had the oil cooler, whereas, the LE and SE did not.

Yes the SSE had the oil cooler. Lines on the drivers side.
Have you lookied into having a new tank intalled?
Thats what I did. Still running strong.

from experience, 1991 has a thicker core also...