You don’t need to spend a whole lot of money to build and program a robot. The Stumble-Bot is a walking cardboard robot that uses servo controlled legs to get around. They are controlled by the Adafruit Crickit. You are going to need a Circuit Playground Express, TowerPro SG-5010 Servo, battery, and a couple of other components to pull this off.
You can find the parts and instructions on this project on Adafruit.