This reminds me of when kids want to learn how to program, it is to make videogames. This has similar complexity for someone without programming knowledge.
So off the top of my head, you'd have to understand data communication through a 3G modem. I haven't got much knowledge about it, but I'd say that this is probably hard with the 8 bit Arduino.
Then you'd have to know about motor controls and somehow work that into saving battery life. Then you have to calculate a big enough car to carry all these and the extensible solar panels and most importantly, the batteries. Remember, the solar panels would have to be big enough to provide enough current to charge the batteries, this may become a problem.
So, start by making a car. Maybe you can control it with a wire and some potmeters to start with and to get some basics as driving the motors and reading analog inputs.
Then, maybe make the controls with an XBee or, why not, with a wiFly module. The best XBees out there can probably reach further than the Wifly. This will give you some insight on how to control the car wirelessly.
With the WiFly module, you can also begin to program the interface software for your computer. Since the Arduino won't be powerfull (or fast) enough to be controlled and work as a webserver. So some form of faster telecommunication needs to be in place. Also, the least amount of data you send, the better so that if this ever comes to life via 3G, you'll pay less for data.
Remember baby steps and you'll get there.