The best way to handle the camera requirements is to use the Arduino as an interface controller, connected up to a some other computer to handle the processing. This computer can be on-board or external via some wireless means. If on-board, you could use a stripped down 802.11b/g/n router, then interface one or more IP cameras to the router; command control would come from a remote PC with custom control software.
Alternatively, this on-board computer could be something like a BeagleBoard or a MiniITX (or smaller) PC, running some kind of stack for control (in my system, it will be a LAMP stack, with the webserver on-board - no off-board processing or interface required). In this case, you could still use an IP camera - or you could use a USB camera (cheaper).
Machine vision software can be completely homebrew (not reccommended, unless you are really wanting to learn how to do it yourself - note, entire multi-volume books have been written on the subject - be prepared for an education), or you can use an existing interfacing package. On the open source front, there's OpenCV (http://opencv.willowgarage.com/wiki/);
on the closed source front (for Windows) there's RoboRealm (http://www.roborealm.com/
). These aren't the only options, but they both are among the most popular.
Something to think about out of the gate (before you even build your robot) is how to implement safety shutdown in an emergency (this is especially needed if your machine is large, heavy, fast, or some combo of all three). This is just like critical system software development: Design the security in at a low level, because it is really difficult to patch in (and get working correctly) after everything else is in place. No - this part isn't fun, but neither are property damage or injury. Think about how you will gain control of the robot (or shut it down) should a steering linkage fail, for instance.
When you are testing your control routine, test the system in stages, and test with the wheels off the ground (especially when testing speed/direction control and steering).
Finally - on the topic of a four-wheel car: If you're wanting something powerful yet fairly inexpensive (though you'll have to work out your own method of steering), a 6 volt PowerWheels ride-on toy can be a good option. These can be found used on Craigslist, Ebay, and at thrift stores and yard sales for around $25.00-50.00 USD (depending on condition).
You'll have to think about your platform choice and design carefully; I had originally planned to use a New Bright Toys Raminator platform (large 2WD monster truck), but due to a variety of reasons things quickly shifted to a PowerWheels H2 ride-on, not the least of which was that I didn't feel I could put the battery power needed for running a mini-ITX based LAMP stack, with hard drives, the camera, servos for pan/tilt, LIDAR, the motors, Arduino, etc - the platform was too small for any good run time. The PowerWheels, though, can easily carry 200 lbs - all that stuff is a pittance, and a couple of extra 12 volt SLAs won't make a big weight difference.