So I'm buying a gaming laptop myself for the first time

That's actually not terrible for the price... You could build a far better desktop PC, but if you've made up your mind I'd say that's not too horrible. GT 640 is even quite bad on a desktop, so the M version will probably be quite a bit worse, but you should be able to play most modern games at 720p on low/mid settings.

doesnt look like the one you found comes with an operating system for that price, the cheapest y410p will be a lot better value for your money regardless though i think they charge a tax on top of the price, which would make it on the high end of your budget range.

Definitely add some more money and get this Lenovo Y510P

Looks good, my crappy GT650M runs Bioshock Infinite, Tomb Raider and Arkham Origins on Ultra. Yours is 640M, can't be much of a difference between the two.

For gaming the most important hardware is the gpu.
this said i wouldn't recommend to buy the one you have choosen because from gpu side its almost the same in power according to the one you already own (only little better but less vram), .

I would really look for a model with a better gpu because If i would buy a new notebook at least it has to be better than my old one so I can see an impact on gaming and get better graphics than before, also it will last longer.

My 2 Cents on this topic. I would suggest building a Desktop by buying part and assembling it yourself. This way in the same budget you can build a even stronger, faster and better config computer. You would need a separate screen though. Also you can not take the desktop anywhere.
You can check the best config for your price range here.

Don't.