Heres the kick: Larger graphics memory? This doesn't matter at all unless you're playing at balls-ass-crazy resolutions, AND have a powerful GPU to back it up. A 9500 GT with 8 Gigs of GDDR3 (never gonna happen, but just an example) is still way way worse than a 9800 GT with 512 MB of GDDR3.
Processor Speed? As long as its dual core, is 2.0 GHz or better, and has at least 3 MB of L2 cache, you're set. IMO, I'd go intel, because I just built two budget PC's with comparable specs:
First: AMD Athlon II 5000 (2.8 GHz w/2 MB L2 cache)+ 2 GB DDR2 800 + HD Radeon 4770
Second: Intel e6850 (3.0 GHz w/4 MB L2 cache) + 2 GB DDR2 1066 (clocked to 800) + 9800 GT
Even though the first is overclocked more than the second, it reaches sim speeds of 1 mid/end game Demigod, while the second chugs away at a constant 7-10.
RAM? As long as you have 2 GB of any speed of RAM you are perfectly fine. How much does RAM effect your PC? Not. A. Whole. Lot.
9800 GTX M, GTX 260 M, HD 4850 M, or HD 4870 M
If you want a gaming PC that's NICE, for 1000 Euros (which is like 2000 USD, right?), the laptop had better have one of those cards, or a better one in it. Otherwise you're getting rpped off.
32 bit and 64 bit are the ways that the operating system is designed. Technically, 64 bit is "faster" and can handle lots more RAM. The limit on a 32 bit system is 4 GB. But in reality? There's really no difference. 64 bit MAY experience some incompatibility with some of your programs, and you'll have to look for 32 bit versions if this happens. The only case of this that happened for me was 7zip - it wouldn't integrate into the right click menu on vista x86-64. So I had to go find the 64 bit version. Problem solved.
Windows 7 is the latest and greatest Windows Operating System. According to everyone, its much better than Vista and XP. In my experience, its perfectly fine. It doesnt really add a whole lot, but hey. It works. Windows 7 is "good".
Concrete tips: look for 7200 RPM hard drives. Focus on graphics cards. If you're willing to invest 1000 Euros, then you're willing to google "xxxx bench" and click a bunch of links. Don't trust notebookreviews.com
Edit: So 1000 Euros is $1500 USD. That's a great price range: you can easily get a high end gaming rig, just not alienware. Alienware is incredibly overpriced for what they're giving you, trust me. Here are some recommendations:
http://www.newegg.com/Product/Product.aspx?Item=N82E16834101203 (5400 RPM hard drive, but you can swap it out for a different one if you want to spend the money, or just add another - it has 2 hard drive slots)