At FPS gaming I would strictly recommend a more powerful VGA, as the GTX765M or higher like GTX770M, paired with an adequate Intel Core i7. You budget will allow this.
Actually I also recommend to consider a barebone solution.
For this please have a look to mysn.de / or if you prefer the UK page mysn.co.uk . This is a German reseller of Clevo and MSI Barebones. In your case, have a look to the A503 Notebook. You can configure your equipped hardware and customize your notebook individually.
For roughly 1137 you can have a
XMG A503 ADVANCED Gaming Notebook 39,6cm (15.6")
• 39,6 cm (15.6") Full-HD (1920*1080) Non-Glare
• NVIDIA GeForce GTX 765M 2048MB GDDR5
• Intel Core i7-4700MQ - 2,40 - 3,40GHz 6MB 47W
• 8GB (2x4096) SO-DIMM DDR3 RAM 1600MHz Crucial
• 1000GB SATA-III 7200U/Min HGST Travelstar 7K1000 (HTS721010A9E630)
• 120GB SATA-III SSD Samsung 840 EVO Series (MZ-7TE120BW)
• ohne weitere Festplatte
• DVD SATA Multinorm Brenner
• Intel Centrino Wireless-N 2230 (inkl. Bluetooth)
• Basis-Garantie: 24M. Pickup&Return | 6M. Sofort-Reparatur -DE
• ohne Betriebssystem
• Office 365 30-Tage-Testversion (nur bei Bestellung und Vorinstallation von Windows 7 oder 8)
• Beleuchtete Tastatur DEUTSCH
Sorry for the german config, but I guess you will be able to translate. This config includes an SSD drive and you might also take the better Wifi-Card to also be able to use the 5 Ghz band (Advanced). This config unfortunately misses a Windows operating system, but you could organise a legal copy at Ebay or maybe you already own one, that you could use.
I hope this helps for the first.