Hi everyone.
I've been thinking for the last half hour how to formulate this topic, and I could not come up with a decent way, as fundamentally I miss information about the name of most components, the wiring, and the programming, which I think means 99% of the project. With the hope that you are not offended and irritated by my humble 1% of knowledge (which might also be overestimated), I present my ambitious project.

One 20-25cm tall robot, with 3 main sets of functions. 1. Movement (basic 2/4 wheels system), 2. Tilt and pan head function, 3. Stepper motor control for varius applications. 4. Remote control. Please find attached my photo with my marveling pile of knowledge. Not.
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I did not add more components, as I don't now if I can run 4 tt geared motors, 2 servos, and 1 or 2 steppers of 1 arduino, or I need some expansion thing, or multiple arduinos.

Function number 3 is simple for someone who knows this stuff. Besides the other controls, there will be an extra joystick module for a steppers which when pressed(sideways) will act as a push button and move the stepper in 90 degrees divisions in the coresponding rotational point. 0, 90,180,270. The application of this is multiple, so I would not bother you with details. Like turning a cube on each of its 4 faces, when sited on a table and viewed sideways.

Functions 2 and 1 are for sure something you come accross all the time.

All this remote controled, by either a made from scratch remote, or a wireless ps2/3 controller, or whatever else.
The desired budget is 200 euro (221 dollars,171 pounds), but I think you are much more qualified to define the costs of such a project.

I don't even know where to start the conversation, not to mention the project.

Thank you for reading, and hope to hear from you.
Andrei