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Whatever is on sale with the specs you want for the price you want.
As long as you have 4gb+ of RAM and a modern dual core then web browsing and simple programs are absolutly fine.
It's very hard to judge longevity of a laptop, 'good' brands have had poor laptops, 'bad' brands have good laptops that last years. Same specs wise, who could say?
You may want a 13.3" laptop, smaller usually lighter but still usability and specs of full sized. You will pay a premium for smaller size and weight while still keeping same specs though.
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4gb ram is plenty for usual stuff. you can see how much RAM you're using in task manager, if you dont go over 4gb then you dont really need more.
I'm trying to assess whether your graphics card is actually the problem, because If you're not playing games or video editing then it should be fine. Its a graphics card made to play games, regardless of 2 big monitors, office docs, facebook and youtube come nowhere close. Do you want to explain what you mean by graphics response?
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personally, I'd just drill a hole to stop the crack and leave it. maybe even a jewbilee clip around it if im feeling fancy!