Heres my 2 cents on this...from car guy to car guy, not vendor on camaro5 to car guy.
It sounds like the OP is looking for a great bang for the buck mod that will inspire much more confidence in the handling of his driver. From taking turns to emergency manuevers, he wants the assurance that the car will do what he wants it to, when he wants it to. And it also sounds like he wants to limit his modding to just a couple items since he is not running the car at an HPDE or pushing 400 horse. And lets not forget the original question..."Do i really need sway bars?" since we seemed to have gotten away from that...
During Camaro5festII, I was fortunate enough to be part of the Pfadt Track attack instructor crew and was given the opportunity to ride back to back to back in several 2010's with various levels of suspension mods from stone stock to stage 5's and also everything inbetween....and what an experience it was to truly prove out each level directly after one another. But each time i got into the car and spoke to the driver, one of the first things i asked them was what suspension mods were done to the car. Most were springs and sways or better, but when the driver of car #1 told me it was stock, I cringed and held on to dear life because i knew it was going to be a handful. I think we even scraped the side view mirrors on the road turning in off the highspeed straight.
The next car i got into, call it car#2, was a pfadt stage 2 car (springs and sways package). Beleive me when i tell you this, it was a completely different car, no BS. Turn in was crisp and clean, body roll was minimal, and the car felt light years tighter than the stock camaro i just got out of. I even asked the driver if he had sub bushings in since the suspension felt very "clean" and he said, "no, not yet, but its on the list." The driver was extremely new and it was their first time on a real roadcourse but regardless of being green to HPDE's, by the 3rd lap, he was really starting to hang this car out and pick up speed passing others. By reducing body roll, balancing the car, and tightening up the response, the springs and sways package inspired confidence in his driving and the driver knew that the car would do what he wanted it to, unlike a stock set up.
I dont disagree with JusticePaul at all with suggesting the bushings. I think they serve their purpose and are a great basic upgrade to help improve handling and rear step in every camaro. But if I had to ride with a leadfooted new driver on a highspeed roadcourse and had a choice of either a springs and sways package vs a sub/diff bushed car, I (and my blood pressure

) would take the car with the springs/sways package any day of the week. And that thought can be applied to spirited canyon carving. I hope this puts it into perspective for whatever the OP's goals may be.
So with that all being said, to the OP, YES, you need sway bars, but thats not all you need.
Just a real world experience.
John