I must be the only 13 year old kid that hates the pi and its associates, yes you can do loads with them, but for me they take away a level of control and thought. You might as well just use a pc and a usb cable to some board or other, yes not a popular vew but I prefer MCU's and bare pcb's waiting to be turned into life.
As for a web controlled robot, the world is your oyster, pick a mcu with a built in mac and phy or get an external one. Adding web capability to a project doesnt need a pi, there are even pics with all the goodies built in and a free stack.