What games will you be playing? This is likely to be the main determining factor in choosing the right one because a laptop with decent graphics is likely to have a good overall spec too & so will do almost anything else you need. Get one with the best graphics you can afford as this is not usually upgradable in the majority of laptops. Another downside with good laptops graphics is that it's the one thing that can raise the overall price considerably, so for £500 you could be disappointed with the graphics you end up with.
For a start, have a look at these links, which are to do with laptops graphics performance with respect to games: click here
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