I always prioritise graphics because it's the only thing I reckon I'll push due to a little gaming. Internet and word processing doesn't exactly require 64 core possessors and a thousand gigs if RAM.
What I always do is go to Ebay and search laptops in my price range.
Then I go here
www.notebookcheck.net/Mobile-Graphics-Cards-Benchmark-List.844.0.html
And then I get a feel for the top graphics cards in my price range. I'll list the ones I find and cull the shittier ones.
Then I'll go back to Ebay and search laptops for the GPU, eg GTX 660M, and see what I find. I'll also look at some of the GPUs that rank a bit higher and a if I can find them in a laptop at a good price.
I generally limit my searches to Toshiba and Asus laptops just because they tend to have higher reliability. But others aren't too far off so whatever floats your boat.
I've noticed that Toshiba 'gaming' laptops (Qosmio) tend to be more multimedia laptops with nicer sleeker design. However the Asus ROG (Republic of Gamers) laptops are indeed more geared towards gaming, usually packing the best gpu for the price range. I originally had a 15" Qosmio with a first gen i7 and the overheating is just too much to bear 3 years later.
I've also noticed that these gaming laptops tend to be 17". The 15" laptops seem to not offer the same performance for price, maybe because it's more compact. They're probably going to be heavier too and require a good laptop bag. So you might have to prioritise performance or convenience for price.
I actually just bought a new laptop a couple weeks ago. An Asus ROG G750JW for $1500 (AUD mind you, I thought Finland was ***8364;?...). But basically anything with similar GPU performance was significantly more expensive, so it was best performance for the price I could find anywhere. Now i'm not at uni I went with the bigger laptop at 17". Heavy too, but i'm not carrying it much so it's fine.
That seems a bit out of your price range, but I would go through the same process of prioritising GPU.
CPU considerations: Celeron = go die in a fire. Current 4th gen (Haswell) processors have better power efficiency and generate a little less heat.
RAM: 8GB. No more. No less. Ok 4GB should be fine for non serious gaming. If anyone tries to upsell you more than 8GB RAM, you don't need it unless you are into serious video editing. Which you obviously aren't. No matter how much they think you need it, you don't.
I spend a good few hours finding a good laptop.
