Don't buy a laptop if you want to game and don't have more than two grand to spend. Cheap "gaming" laptops are utter trash.
Build a micro-ATX system in a small case if you don't have much room. Your budget's a bit small, but it shouldn't be hard to build a really strong, if last-generation, system under $1k, especially since your needs don't seem to be too taxing.
Mainboard, $45
http://www.amazon.com/BIOSTAR-H61MGC...micro+atx+1155
Core i3 CPU, $100
http://www.amazon.com/Intel-i3-2100-...s=core+i3+2120
nvidia GTX 650, $105
http://www.amazon.com/EVGA-GeForce-1...rds=gtx+550+ti
RAM, $37
http://www.amazon.com/Corsair-PC3-10...ords=ddr3+1333
HDD 1 terabyte 7200RPM, $100
http://www.amazon.com/Western-Digita...1tb+hard+drive
Monitor, $120
http://www.amazon.com/ViewSonic-VA22...onitor+21+inch
Case, $81
http://www.amazon.com/Thermaltake-La...micro+atx+cube
PSU, $35
http://www.amazon.com/Cooler-Master-...t+power+supply
Keyboard, Cherry MX brown switches, $79
http://www.amazon.com/XArmor-U9-Cher...nical+keyboard
Mouse, $38
http://www.amazon.com/Logitech-Wirel...=logitech+m705
Total: $740 (before shipping). You cannot find a laptop this powerful for anywhere under $2000, and no laptop keyboards (not even the legendary ThinkPad keyboards) can hold a candle to a mechanical switch keyboard with Cherry MX tact switches. The monitor is full HD, the video card will more than play the games you want to play, plus you've got 8GB of RAM and 1TB of storage space to fill up with fansubs and game installs.
It doesn't include an OS, of course, so you'd have to furnish Windows or use some variation of Linux. OEM copies of Windows 7 are disappearing as Microsoft is leaning on retailers to clear their stock and sell only Windows 8. If W8 doesn't bother you, the OEM copy is usually $100, which is a pretty steep discount off the normal price.
If I were you, though, especially since you want to game, I'd check Craigslist and eBay for Windows 7 64-bit for System Builders (also known as an "OEM copy"). A lot of the retailers that Microsoft forced to ditch their W7 inventory will need a place to dump them--they tend to turn up on CL and eBay.
Linux is a great free alternative if you don't need Windows. My personal favorite distro of Linux is Linux Mint. Totally recommend it.
The newest iteration, Linux Mint 14 "Nadia" (especially with the Cinnamon window manager) is very easy to use and very nice to look at, not to mention has snappy performance and I really prefer it overall to Windows 7 or Windows 8. Sadly my large investment in Steam games leave me stuck with Winblows, at least until Valve can convince more devs to port their games to Linux.