Hi,
I suggest you watch the heat treatment oven build series from Libris knives on YouTube. He does a really good job of explaining everything. Also if you don't have basic understanding of electronics or electrical, I wouldn't suggest you do it yourself. Wiring up a PID controller is pretty standard stuff but you're dealing with high voltages, which is why I would suggest you find someone who could do it for you if you're not sure.
It has 3 basic components, the thermocouple, PID controller and the SSR (or contactor relay). The PID is a closed loop control algorithm that decides when the elements should fire in order to reach the desired temperature and hold without a lot of overshoot (after proper tuning ofcourse). The SSR is basically a low voltage controlled switch. It takes a low voltage to turn on/off the high voltage mains supply to the elements.
In your case start off with a cheap PID controller and you can upgrade to the expensive ramp and soak timer ones later if you'd like. There are literally dozens of them out there and you need to dig around a bit to see which one you want.
Also since your elements are drawing 30 amps, you need a good ~60 amp SSR with a beefy heatsink and some ventilation in the control box. Make sure you go with a good quality SSR because the cheap 40 amp SSRs that I've seen ended up having only a 16 amp triac inside.
Then there are a couple of safer features like door open kill switch and all which I think you could use from your existing kiln. Again, he does a good job of explaining all of this in the YouTube videos.
