Laptop For Final Fantasy 14 (Single Player games too)?

Usually anything that goes beyond the game's video card requirement will also go beyond the rest of the requirements, as the video card is usually the most expensive part in a laptop (And thus the company will get the rest up to speed first, if you wanna look at it like that)
Any $1,000 laptop should, in a moral world, get you decent gaming (No anti-aliasing, or anything like that), but to compare I've got an ~$800 HP DV-6 model that does me quite well.
Things you'll look for to get the best value:
A LOWER resolution -- Laptops aren't designed for super high resolutions when playing games. Something around 1360x768 is prolly ideal.
Something ABOVE a Radeon 4650 -- This is one of the most common cards in a laptop from what I've seen, and plays decently at 1360x768, but if you can go higher, do it.

Again, the main one is the video card, since most games only need 2GB to play smooth and very few games will ever max out a processor noticably.

Don't go by the "Recommended" specs on the box of a game. Crysis suggested GPUs that were available a couple of years ago, but we're just now getting past the point of playing it. Just food for thought.