PID temperature regulator with arduino (temperature speed decrease and increase with time) for oven

I need a PID temperature control for a lab oven ( resistance around clay) where the temperature increase and decrease with time at different speeds (1 to 20 hours ; up to 500 degrees celsius) . I need the ability to have multiple settings entered at the beginning run one by one without user interference (speed 30 degrees per hour (0,5 per minute) until hour 5, we reach 150 degrees then 50 degrees per hour until hour 7 , we reach 250 degrees, then stay stable at 250 for 3 hours and so on ( up to 5 settings) . I need arduino code + proteus simulation. I have keypad 4*4, max 6675 + thermocouple type k, display ssd1306 or 2 lcds or any of your prefernce, for other components you have the freedom of choice. Budget is 100 USD.