I want to build a rover with a simple camera, does not have to be HD.
I want to build a "ground control" with an LCD that would receive the camera feed and to be able to steer/accelerate the rover.
I have looked at xBees and other bees but I have no understanding how or what Arduino can transmit. If the transmitter/receiver can handle the bandwidth and if the cpu can take it (ATmega328). In the beginning the range does not have to be 1 mile.
Should I go with standart computer wireless? I don't want to connect it to a modem or internet, just my "ground control".
Wireless web cameras exist, and there are Arduino shields with video cameras integrated with cellular modems which can be accessed from the internet. Your requirements are very vague, though. If you don't want a range of a mile, what range do you want? Would a WiFi range be acceptable? That's probably the best you're going to get without expensive transmitting/encoding equipment or going via a cellular network.
I would personally immediately give up on the thought of trying to transmit the video portion through the Arduino. Just get a wireless camera and receiver with the range you want. Keep the video part separate.
Now, you want two way communication for everything else. The xbee is a well supported (lots of example code, shields, etc...) wireless transceiver for the Arduino for doing that. This would handle the transmission of your RC commands, sensors or whatever else you plan to have on your rover (like turning on/off the camera, IR LEDs, Pan/Tilt.)
You are probably going to want to overlay stuff on the video. For that, look at Video Experimenter: Arduino shield that lets you do all kinds of experiments with video (but there are plenty of other projects out there just google 'arduino video overlay'.) This would allow you to use a single LCD for both the video and for status messages or whatever else you want to display.
As I always recommend (well, really it is absolutely essential), sit down and spend some time thinking about your project and draw up a block diagram. Once you have the block diagram, break out the 'blocks' and define each one. Once you can't break the project down any further, then start working on one block at a time.
For example, at the very top level you will have your rover and your ground station. For each one, you need a block diagram of what is involved in it. Both are going to need power supplies. This would be a 'block.' At this point, you don't need all the specifics of how that block works (and usually this is the last block to define because it will depend on the power requirements of the other blocks.) Within the rover, you will have your camera and a transmitter. This is a block. To define that, you need to find an appropriate camera and transmitter that will fit your requirements (weight, resolution, range, power..)
Etc... etc...
Maybe you have done all this already, but it doesn't appear that way from the vague description you have given. But if you have not, you need to do this before you even start buying anything or even asking what to buy.
Should I go with standart computer wireless? I don't want to connect it to a modem or internet, just my "ground control".
The below is some tinkering I did for making a simple routerbot that would be web controlled between the wireless router and a wifi capable device . using a wireless router adds the possibility of easily incorporating video.