A lot of your requirements could mean anything...
E.g. what are you doing with MATLAB? I have a laptop for matlab use (for my job) and it's not a cheap one! But you'll have different (almost certainly lesser) requirements. But depending on what you want to do with it, good linux support for the laptop might be on your list. If you're just using "standard" matlab and not dicking about with too much mex action then you're probably fine with any OS though.
If you're on student matlab, you're limited to 32bit IIRC so more than 4Gb ram doesn't help you there.
Similarly, how much are you actually editing HD video, what software etc? No point blowing all your money on a discrete GPU if you can't afford the software to take advantage of it, or if it just speeds up a job you only actually do twice a year and could go and grab a coffee whilst it's processing etc.
FWIW I quite like win8 with touchscreens, though I've only used other people's machines as my work stuff's all win7 or ubuntu and my home kit is OSX or ubuntu.
Take a look at the dell outlet store though (remember to add VAT to prices!) both the home one and the business store - the business laptops tend to be better made. At the higher end at least, can't say I have much experience with low end ones.
You said "cheap" but what's your budget? Pretty much anything will do what you want, but might not be brilliant at it. But then clearly something to be brilliant at HD video editing and matlab is out your budget.
E.g. quick look on dell outlet, about £700 all in gets you 8Gb, quad core i7 up to 3.2Ghz, 2Gb 640m GPU, 1080p screen and a 750Gb HD with 32Gb mSATA SSD cache.