Adding a turbo to an otherwise stock 2.3 can be done, but if you want it to survive for any length of time you'd have to keep the boost levels very low (6psi max) giving you very little in the way of horsepower gains.
Nitrous is an option with the 2.3, a good one if the car is mainly going to see street time and only some occaisional drag strip usage, but don't expect to run with the big boys in their 5.0 and 4.6 Mustangs or LT1/LS1 Camaros and Firebirds, 25hp or 50hp nitrous kits are safe on these engines, and will give you enough power to feel a difference, without being too hard on parts (assuming you don't have an automatic, if you do, forget about racing the car, the stock A4LD automatics that came in these cars won't even hold up to any abuse behind a bone-stock 2.3) the stock 105hp of a 1993 2.3 + a 50hp shot of nitous puts you on par with some of the easier to pick on import fair (non Vtec Hondas and Acuras, mid 90s and older Toyotas that are running 4-cylinder engines other than the 22R family, Mazdas with non-turbo engines smaller than 2.2 Liters, most Nissans from the late 90s back with four-cylinder engines, Volkswagens (be careful with those though, some V-dub owners are tricky, I know where there's a 1972 Beetle that looks and sounds bone-stock but runs 11s) and similar cars.
If you really want to put power to the pavement with a 2.3L Mustang, you need to swap in a 1984-1986 Mustang SVO or 1987-1988 Thunderbird Turbocoupe 2.3 Turbocharged engine. These engines were built, internally and externally to run a turbo (much better internals, including forged pistons instead of cast/hyperutectic, connecting rods based on the old 289hi-po design, oil feed bosses already drilled into the block and head for the turbo, etc.) You'd also want to swap the computer and wiring harness from said car, and if you've got an automatic now, you'd also want to get a 5-spd
tranny. The 2.3 turbo family ranged from 175-215hp stock (most of the changes were merely tuning changes in the ECMs) and in a fox-chassis Mustang of equal weight, run nearly dead-even stock-for-stock with a 5.0 in the 1/4 mile while getting better gas mileage to and from the track!
Dig around in this forum and the 2.3L Talk Forum (The search feature at the top of this page will be helpful) there are several other threads covering all the details of what can and can't be done with the 2.3L engine, including carbureted 2.3s, turbocharged, nitrous-sprayed, and fuel injected.