Start small! If you haven't used Arduino before, it will take a while to learn to how to handle the various sensor types used to read temperature and humidity, and decide which might work for your project.
Then you can start thinking about control. PID control is usually needed, and there is a learning curve for that. It is a challenge just to keep the temperature of an object constant, so master that first for a small object, using a resistance heater.
Humidity control will be a much more serious challenge, and can be saved for last.