I'm not sure where to start with this, but you don't seem to indicate what level of electronics experience you have? What have you built in the past? Do you understand Ohm's law? Are you familiar with a multimeter (do you even own one)? Are you familiar with troubleshooting electronic circuits? Do you understand how to read a schematic? Do you understand basic electronic components and how they work (ie, resistors, diodes, capacitors, transistors, etc)?
If the answer to any of the above is "no" - then before you should even attempt "Goal 1", "Goal 0" should be to acquire the above knowledge (and then some).
Without that level of knowledge, you'll be spending gobs of money as you burn up, blow up, short out, etc - parts and other systems, without understanding why such things are occurring. Note that even with that knowledge, you will still have such incidents; hopefully at a much lower rate, though. Just realize that electronics, and especially robotics, can get expensive quickly, depending on how and where you go with it.
I would urge you for your first robot platform, to start out small, and pre-built: Look for an old radio-controlled car toy (look for Nikko or New Bright R/C truck chassis - they form great platforms; alternatively, if you can find one, a small radio or remote controlled differentially steered tank platform is a great option) at a thrift store or Goodwill or such (shouldn't cost more than $5-10.00 USD), and build your first robot on that platform. Just make sure that you "test" the drive train and steering system by carefully and slowly moving the parts, listening and feeling for the "bad sounds or movements" of broken components; if it's broken, skip it and look for something else. Make sure, though, that you only buy something that looks kinda like a standard vehicle - as noted, a truck or a tank works best; skip any strange looking toys; you might also want to skip it if it is a low-slung car, or something that looks like a dune-buggy or sand-rail vehicle; low-slung cars can't work well on carpeting, and the others might have too much speed. You don't want "snails-pace", but you don't want something "out of control", either.
Attempting to build a robot platform from scratch (that is, buying the materials, motors, gearboxes, wheels, etc - then machining/assembling them using hand and power tools), if you don't have any experience at such mechanical construction, can become an object lesson in severe frustration. Of course, if you have this experience (you don't say), then it becomes easier. If not - building small robot based on a pre-existing platform will relieve you of this frustration, as the work is already done for you. All you have to worry about is interfacing the motors and steering system to the Arduino.
One other thing to mention once you get to the point of developing your robot platform: Perform all testing and development at the beginning with the "wheels off the ground" - put the chassis up on a small stand or something. This will keep you from accidentally driving it off the desk, dragging you soldering iron and everything else off as well, and destroying your Arduino. This kind of advice applies whether you are building a small desktop rover, or a full-size autonomous automobile. In many cases, though, you can perform testing without being connected to the drive motors at all; just substitute in LEDs for indicators of direction and control outputs.
There's a ton more than this, though - I could go on for ages on this subject. There are a ton of books out there that you would do well to pick up and read, not to mention magazines (and of course, web sites). I hope this helps, and good luck with your projects.