Given a straight choice between Asus and Advent, I would go with Asus, purely on the basis of reputation, but that's a personal choice.
Your ease, or difficulty, of finding a suitable laptop, depends on YOUR definition of your words "video" and "some games". Most laptops, with a reasonable dual core processor, and basic discrete graphics, are going to be capable of some video editing, and playing very basic games. But, if you are talking about good performance at video editing, and gaming, then your choices will be much more limited (and maybe impossible at your budget).
If you can give some indication of what YOU mean by "video" and "games", eg what games, it may be possible to give more detailed advice.
Certainly agree with Woolwell's advice, on other manufacturers to look at.
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