When I lowered mine, I did the springs, shocks, upper and lower control arms (UCA/LCA), and adjustable panhard bar. My rear suspension is different from yours in that it has three pieces while yours has four. So I put in two solid LCA's and one adjustable UCA. You have a four link suspension, so you'll need the appropriate parts. The reasoning behind the adj. UCA is that when lowering the car, the angles and geometry changes. So to correct the pinion angle, you'd need an adjustable part. Same with the adj. panhard bar. It centers the rear end.
It is also recommended that you get LCA relocation brackets, but I ran out of money so I don't have them
Hmm phone just rang. Lost my train of thought.
Also, you should check the alignment up front. When I did my springs, I just had the Ford dealership check the alignment, and it was pretty close to normal, but if it is too far out of wack and can't be fixed with the stock hardware, then you may need Caster/Camber (C/C) plates or camber bolts. The cc plates run around $200, and the camber bolts are about $40. But have the alignment checked first before buying parts, as you may not need to fix it. I took the alignment chart/specs to a local & reputable mustang shop and asked them if I needed to worry about it, and they said no. And the dealership agreed (though the dealership also said they wouldn't install cc plates since it's aftermarket).
I just grabbed some chocolate and got distracted again.
Here are some links to help you get started
Control arms:
1999-2004 Mustang Control Arms at AmericanMuscle.com - Free Shipping!
cc plates
1999-2004 Mustang Caster Camber Plates at AmericanMuscle.com - Free Shipping!
shocks: I got the orange Koni STR.T ones. I'm happy with them. But you could do whatever you want after researching more
1999-2004 Ford Mustang Shocks, Mustang Struts at AmericanMuscle.com - Free Shipping!
I'm not seeing any panhard bars for your year, so maybe that's different too :dunno I'm seeing some torque arms that look like they do something similar. But more people will stop by to help
:welcome to the forums also. I used to be in Tn