Haven't been working on them long, so take my advice with a grain of salt. If anyone contradicts me, I'm probably wrong.
Mustangs in general are pretty reliable, within the usual limitations of age and abuse. They also have a reputation of being easy to work on. I've heard in a few places that the Mustang aftermarket is the biggest of any car model, and Ford is generally friendly to that aftermarket.
Don't know how old you're wanting to go, but before 1994, the "GT" name didn't mean nearly as much. They put the V8 and the enhanced drivetrain in a lot of base models back then, and those base models are actually more desirable for some people, particularly the notchbacks. In 1994, they moved to the current system where "GT" is equivalent to "V8 engine".
If you go really old, the 302/5.0 Windsor engines from about 1983 onward were mated with a T5 manual transmission. The engine in stock form pushes the T5 pretty close to its limits, so any power mods may result in broken transmissions. They did make some changes to the T5 over time to increase its capacity, and the aftermarket has done some things as well. Starting with the 1996 model year, GTs went to the "Modular" 4.6L engine and an upgraded transmission.
GTs between 2005 and sometime in 2008 have an... interesting spark plug design, which results in spark plugs breaking off upon removal and leaving some of themselves in the engine. There's a special procedure for removing these plugs which is supposed to help avoid the problem, and special tools for extracting the left-behind pieces when they do break, so it's not a total disaster if it happens, but it's not fun. They redesigned the plugs for the 2008 model year, but I've heard rumors that some early 2008 models have the old design.
There were complaints about the manual transmission in 2011 and later GTs, but I don't know whether those complaints were just about shift feel, or if there were actual problems.
Those are all the things I know about.
