Generally you want to "overbuy" your laptop. Theory is that what you buy now will last you a long time, so you don't want to buy something that isn't up to snuff now only to pay another $1000 the next year or regretting your current purchase.
For video editing and processing Photoshop elements you're going to want an i7. And not just any i7; the best you can afford with and high end graphics card. I'd say Nividia's 750M and up would be high end stuff.
In terms of sound quality, the speakers of most laptops are... fairly bad. Yes you can get good ones but you might have to trade off stuff to get it. You could go for a headset with an external sound device plugged into said laptop and get leaps and bound better audio quality than the laptop's speakers.
HOWEVER: If you need a machine that can last a decent amount of time between charges then you'll be needing to slim down a bit. You can find U series i7 that will give you better performance than some M series i5 machines. Looking at reviews on Notebookcheck.net is also a good place to find reviews of some of the laptops you're looking for be they ultrapowerful gaming machines or sleek power sipping ultrabooks.
As far as graphics goes I know there exists LP versions of some of nvidia's mobile graphics cards (i.e. LP 640M) and odds are that those will do you justice as well. Note that most laptops
on battery will not engage the full use of graphics cards for the sake of maintaining battery life.
In terms of what to buy specifically, I'm going to take a leap and say no to the Alienware, but feel free to get it. They usually come with price premiums, but so is the same for almost every gaming themed laptop.
Lenovo has a 510p that has dual 750's as an option with a slimmer chassis, and it comes with an i7.
http://shop.lenovo.com/us/en/laptops/ideapad/y-series/y510p/ (keep looking, it's in there somewhere)
for 1200 you could also get a decent custom machine from the likes of Xotic PC or others of the like. There you can find options for different processors and graphics.
If you have any more questions, ask. Buying a laptop is going to be tough and a very personal choice due to what you need it for.