The people recommending coil overs aren't paying attention. The guy is asking for budget solutions for a driver. Also, coil overs aren't "essential for a smooth riding car". Don't get me wrong, with the right parts, that would be the dream, but I wouldn't describe them as budget friendly.
As far as a shop recommending against the Shelby/Arning drop: time to find a new shop. That's just bad advice. The drop improves the suspension geometry and makes for a better handling car. Period.
Disclaimer: if you can afford to work with Street or Track/Opentracker, do that. Great guys that shoot you straight and have taken a lot of the guesswork out of things. I'm a fan of the blueprinted upper control arms if you don't trust yourself to set them up.
I did exactly what you are describing. In my case, staying within budget meant doing a little leg work myself and sourcing parts from multiple places.
Upper and lower control arms: Moog brand parts from Rock Auto
Sway bar and bushings: Stay with rubber bushings, not a bad time to upgrade to a thicker sway bar.
Buy the best shocks you can afford. I make KYB's work, but they are crap compared to Bilstiens. Easy to upgrade later though, so that's my plan.
Spring perch: I went with the "improved" Scott Drake perch that isn't a roller bearing, but does move much more freely. I'm sure roller bearing is better, but going from stock to this version was like night and day. Not bad for half the price of a roller solution.
Strut Rods: Adjustable would be great if you can afford it. I couldn't at the time, and just put fresh rubber bushings on and it's still a vast improvement with the other parts.
Springs: your milage may vary here depending on desired firmness and ride height. A set of GT spec springs would probably be a good idea.
Rear: it all comes down to the right kind of steel, and the consensus is that Eaton is the end-all, be-all for springs but you pay for it. Might be worth it to you to get some new budget friendly springs just to keep it from bottoming out on you and plan to upgrade later. I have some 20 year old Mustangs Plus springs and they kind of suck. Very firm and bouncy. But they work.
Last bit of advice: Do this work yourself if you can. This is an easy weekend job if you take your time and you'll learn a lot about your car and how things work.
The anvil of reality.