I just noticed this thread was here. I'll go ahead and make a list of things.
Lenovo's a pretty solid brand. This has a dedicated GPU, but it's considered Low End because of the price and fact that it's going to run hot with AMD as your graphics unit. This specific laptop boasts an impressive Quad-Core processor, but only running at 2.00 GHZ. If you're looking to play runescape, some small steam games, word process, or run photoshop in short bursts, this laptop will work for you.
http://www.newegg.com/Product/Product.aspx?Item=N82E16834319445&leaderboard=1
If you're looking for something artsy that you can detach the screen from and use as a tablet, I recomend this one. It's excessively low end, so I really only recomend this for the occasional photo manip.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=9164838&CatId=219
On the flip side of that, for 800 dollars you can get the good version of this setup. This computer boasts a dual core i7 clocking at 2.4 GHZ. Perfect for most small activities and basic gaming such as Guild Wars, Starcraft, and many Indie Steam titles.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=9618828&CatId=219
Let's say you're looking for an actual gaming system. I always recomend desktops for this, but if you absolutely have to get a laptop the N550JK is a good buy for the money it costs. It boasts a GTX 850M Nvidia Graphics card, 15" screen, 5.1 surround speakers, and a 2.4 GHZ i7 Quad. The battery is a little lackluster at only 4 cells, but for 800 dollars this is a deal. You'll probably be able to play Skyrim on high.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=9095406&CatId=3998
So let's say you have a budget of about a thousand dollars. This is where you'll throw down the real money for a system that can play some current-gen games. Whether you're using this one for LOL/DOTA, or getting down in the dirt with Phantom Pain, this laptop will run your games solidly. This computer is a 2.6GHZ i7 Quad with auto turbo boost to 3.6GHZ, GTX 960M Nvidia Graphics, 16GB of DDR3 Ram, and packaged in a very attractive shell.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=9637334&CatId=3998
On the flip side, if you're willing to drop a bit more.. maybe around the 1.5k range, then you're going to have the closest thing to a desktop replacement you can get. This machine is very similar to the last one, except it has a 17.3" display, 24GB of ram, and being in the Asus ROG family, you're gaurenteed great cooling, hardware, and display. This machine is HEAVY, as it's meant to replace a desktop.
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=9514707&CatId=3998
So what if you have more than 2000 dollars to spend? Well look no further I have the perfect solution. Buy a desktop. Seriously. My current build is a 6 core processor, GTX980TI, 32 GB of DDR4 Ram, and a wonderful case for 1,700 dollars. Your best bet after 1500 is just to focus on a floor unit that can be upgraded and kept in with the times.