[84LX89GT]

First i'll start off by saying, buy a 5.0L mustang, it's MUCH cheaper than trying to convert a 2.3L unless you have a parts car or access to cheap parts.

That being said:

Every trans made for a 2.3L is too weak to stand up to a 5.0 under any kind of abuse or for any extended amount of time. the C3 automatic trans is an obsolute must to replace, older 4 cylinder T5's can be made to work, but have a low torque rating that they can stand up to: so basically, trans must be replaced.

Also, you'll have to replace:
Motor Mounts, switch to a 2 or 3 core radiator, hook up all applicable wiring and figure out how to make ignition system work (duraspark II you may need to change modules, but i'm not sure on that). You'll need also to rewire tachometer system (if you have a tach) and any miscellaneous wiring such as sensors for gauges. You can still run the stock 7.5" rear differential, but it's known to fail under any kind of abuse, plus it has the smaller drum brakes than an 8.8" rear would have.
Older 5.0L mustangs (up till '84) had the same braking system as the 4 cylinders and i can tell you from experience that is a VERY bad thing as you have alot more speed and weight to deal with. Also the 4 cylinder suspension is way softer than the 5.0L handling package suspension. At the very least whether you switch engines or not, buy a rear sway bar from a 5.0L and install it on your car, the handling increases by 10x.
That's all i can think of off the top of my head, i'd save up for a 5.0L or find a wrecked 2.3L turbo powered car such as a thunderbird turbo coupe, '83-'84 Turbo 2.3L mustang, '84-'86 mustang SVO or Merkur XR4Ti.