What kind of graphical demands would your "casual gaming" entail? If they are light enough for integrated graphics, I'd go for a ThinkPad T540p - customizing one on Lenovo's site now, it's $1290 with a "3K" IPS display ($200 less if FHD TN is sufficient), i7-4710MQ, 4GB of RAM and a 500GB HDD. Use the remaining ~200 of your budget to upgrade the RAM and add an SSD, and you'd have an amazing powerhouse of a laptop that should last you for years. If the integrated Intel graphics aren't enough, you can add a GeForce 730M for $130, bringing the total with the 3K display to $1407 or $1227 with the FHD display. Personally, I'd go for the FHD display and 730M, add a Crucial MX200 250GB for another $110 (Newegg), and 16GB DDR3L for another $110 (also Newegg). That brings your total to about $1450, not including shipping. If you're able to skip the dedicated GPU, you could even get the i7-4810QM, which gives you higher base and turbo clocks, plus a higher clocked IGP. Or, of course, you could go all-in, with the i7-4810QM, dGPU and the 3K display for $1530. With the SSD and RAM upgrade this brings you a bit above budget, but you'd be getting a superb laptop. Oh, and I'd recommend adding the Intel 7260AC wireless card over the standard Thinkpad 2x2 card.
ThinkPad quality is pretty much unbeatable, and the T series gives great bang for your buck as long as you're not fussy about weight. Sure, you can get cheaper laptops with the same components, if not better. But they will not last as long, nor perform as well over time.
Of course, if you need more powerful graphics than the 730m, you're out of luck with the ThinkPad T series.