The 88-105 HP models are Normally Aspirated - No turbo.
87-90 (I don't recall what the 4-eye models were rated at N/A) have 88 HP and utilize a distributor. 91-93 Models have some head revisions (dual plug head), a different cam, utilize a distributorless ignition system (DIS) and produce 105 HP.
Although you can swap a 2.3L Turbo into any 79-93 Fox Mustang, the easiest ones to do are the 87-90 models. The 91-93 models are more difficult because they have some differences in the wiring, however it can be done and the required modifications to the wiring harness are well documented.
The easiest, cheapest way to improve the performance of an 87-93 2.3L mustang is to swap in a turbo engine from the Thunderbird Turbo Coupe ('83-'88, with the 87-88 models being the most desirable) or to get a turbo 2.3l out of a Mustang SVO or Turbo GT. Although there is little difference, the Mustang parts are generally more expensive.
Why can't you slap a turbo on your N/A 2.3L Mustang engine?
Answer: You could, but the cast pistons are weak (the Turbo engines use Forged pistons) and create a higher compression ratio that creates a higher chance of detonation, which is the number one cause of engine failure in a boosted application.
Your N/A block, rods, and crank are up to the task of supporting a turbo, so if you were to rebuild the engine using quality pistons, then all you have to do is add the turbo drainback to the block (it is already machined in a turbo block) or simply add the drainback to the oil pan.
Some people like to rebuild the N/A motors due to availability, or because they want the increased displacement from a later Ranger 2.5L engine, which is simply a stroker version of the 2.3L.