The questions you ask can be answered in different ways and are a bit subjective.
-How important is CPU speed?
It is as important as the programs you will be running. Some games are more processor intensive and will slow you down if your processor is lacking, while others are paimarirly GPU based and will slow you down if your GPU cannot keep up.
In general GPU is much more important for a gaming computer. However, some games are quite CPU intensive as well and will be slow even if you have the very best video card, but a lacking processor.
For your particular case, I say AMD. They usually have higher performing GPUs than Intel, but have lacking CPUs. Assuming you are using hybid gaphics/processing (same chip).
-I know the GPU should have dedicated memory, is there a certain amount I should be looking for?
I would say 1GB should be fine, but no less than 512 ideally. However, this primarirly depends on screen resolution.
I know this is abit outside your price range, but this would make a decent gaming laptop.
I will update later if I find a better laptop or a better price.
It is $940
iBUYPOWER Computer :: 2012 Halloween Battalion 101 CZ-13 Gaming Laptop
Here are two more suggestions:
$880 - http://www.newegg.com/Product/Produc...82E16834215672
$780 - http://www.newegg.com/Product/Produc...82E16834214496
Edit2: I think that the Acer ($880) offers the highest value of the three laptops in terms of gaming, if possible, I recommend saving up a little more money for that. If you cannot go as high as 880, for 780 you get a decent set up, but that extra $100 gives you much higher gaming performance with the Acer.