For Extreme Portability and Lightness, the MacBook Air (http://goo.gl/9Q0hD
) would be your best bet, also you could get it with the highest specification for around your budget so this would be great if you could live without the gaming, but if you really do need to play games a bigger more powerful machine would be better.
For Power on the Move, The MacBook Pro (http://goo.gl/2I9k5
) would be great for you, although for your budget you will not be able to do heavy gaming as the 13 inch's screen would be too small and the 15 inch's specs would not be high because of the price.
For Saving Space and low cost, The Mac Mini (http://goo.gl/SO7kC
) would be great but will not have the power of the Mac Pro or the iMac but it would give you money to spend on a good display or any extras/peripherals, but an alternative to this would be to get the top spec Mac Mini for around $1,500 and this may be able to play entry level/basic games and you would be able to also edit videos.
For Good Looks and Power, The iMac (http://goo.gl/OzykQ
) is in budget, with one of the highest specifications costing $1,999 which will be great for gaming and you will not have to buy an extra monitor, also it will have all of the components stored in the screen so it will save space.
For the Gold Standard, The Mac Pro (http://goo.gl/9GKtt
) would be great for gaming, video editing, and any other CPU intensive tasks it will be running Mac OS X which is not the best platform for gaming but you can always bootcamp Windows as I have heard that Macs' make great PC's. The only Problem with the Mac Pro is that the base model is $2,499 which is $300 over you budget but if you can afford the extra cost then this is the way to go.
For Portability and gaming to a budget, The iPad (http://goo.gl/IjU2t
) with Wi-Fi would be good for gaming on the move but the video editing will not be as good as it would on the iMac but it is a good device for light gaming but you will not be able to play games like Call Of Duty: Black Ops or any other heavy games as they are not released for this platform.
For Portability and Web Browsing on the move, The iPad (http://goo.gl/ljU2t
) with Wi-Fi and 3G would also be good for gaming, but you will also get Web Browsing wherever you are in the country, also all iPads act as iPods so you can use it for music during your way to school/college for example.
I think for your budget the iMac would be best as you can play games, do video editing and any other CPU intensive tasks but you would not have the portability, if you really do need it then the MacBook Pro would be best.