What you are attempting to do is create what is known as an "unmanned ground vehicle"; aka, a "UGV" - so if you do some searching on that term, you might find some information of relevance to your project (at worst, you'll find some inspiration - UGVs are typically used by industry, rescue, and military for various jobs).
As far as using an Arduino - yes, you can do this, with the exception of one part (unless you want really low resolution): the camera. You can easily set up an Arduino to control motors and a pan/tilt mechanism for the camera, but the Arduino itself (or more specifically, the ATMega168/328 upon which it is built) does not have the processing horsepower to process a video stream from a camera and send it wirelessly to your PC.
Instead, what you should look into is using an IP camera; depending on how you set things up, this camera can be either wireless (802.11 wifi) or wired ethernet (thru an on-board wifi router).
One thing you will need to determine is the size of vehicle you are planning on controlling, because the size of that vehicle will determine how much battery you can load on it, to power the vehicle, Arduino, camera, pan/tilt, GPS, etc. Whatever parts you do get as off-the-shelf components, you are going to want to strip down to reduce weight (ie, remove plastic casing, etc).
If I were doing this (ah, heck - actually - I -am- doing it; only my vehicle is based on a PowerWheels H2 ride-on, so weight and space isn't an issue; in my case, the Arduino will be for motor control and pan/tilt control initially, the cameras will be USB Logitech Orbit AF units, with a custom servo pan/tilt system, plus a on-board Mini-ITX Intel Atom motherboard - but we're talking about your project, which likely won't be as big), I would look for a large R/C car or platform; if you can swing it, a custom platform made of welded steel thin-wall square tubing, with a custom on-board generator for hybrid-power would work great, but you would likely need a larger motor system and controller - which isn't really suitable for a beginner...
So - get a large R/C car; something like a large radio-controlled 2 or 4WD truck chassis is ideal - something with 4-5 inch diameter tires (sorry about the non-metric units). If you check my site, you will see a toy I used as a early tester kit; it was a New Bright Toys "Raminator" truck - nice and big:
http://www.phoenixgarage.org/show_article/51
A more expensive alternative would be something like a large Traxxas or similar grade chassis; just be aware that such vehicles are anything but cheap to purchase...
So - take something like that, add several 9.6V R/C battery packs for power, set up your camera and Arduino, etc - and you should be able to get something to work. Something you might want to think about is not processing the video or using wifi for the video at all; instead, get one of those cheapo 900 MHz or 2.4 GHz wireless video camera kits like you see all over Ebay for video surveillance, then on the PC end, route the output of the receiver into a video capture card/port; then process the video from that point. Not quite as slick, but it will work, and save you a ton on battery usage (more run time).
You can then use wifi (via a wifi shield or similar) or whatnot for controlling the Arduino (and thus the motors and pan/tilt unit), and receiving other telemetry data (GPS, orientation, etc) back.
Good luck on your project, hope this helps!
