Help me choose a laptop!

[Anova]

This is better discussed in more technical forums such as Reddit or Tom's Hardware. I'm not a guru on graphics cards, but I'm going to give my shots on it.

That CosmosIII should cover most of your needs. I suspect you will do fine on medium settings (although high and ultra-high settings may be difficult). More on that later.

The graphics card is generally used to process physics, lighting effects, and process pure polygons (read: player character models). RAM is used more often to process textures and visual effects. FF14 isn't that graphic intensive in terms of polygon count and physics (especially if you're just running dungeons/raids and not the massive open-world or diadem content). You can also keep this in mind when tweaking your graphic settings to optimize it on your laptop.

There have been reports of people using the HD Graphics series reasonably well for gaming. Nothing spectacular mind you, but it won't crash and burn. That said, the GPU will get very hot very fast and most people do not like the idea of a 70C oven sitting on their lap or burning a hole through their table. You may have to get a laptop cooling accessory if you intend to use it for any length of time (more than 1 hour of playing likely).

Movies and the like require less GPU and more RAM, which is considerably less power extensive and doesn't use the graphics card as much.

I would try to get at least 4gb RAM or preferably 8gb RAM. It's going to let you set a higher resolution and process more effects and players (useful for aforementioned massive content).

If you can bear it, cancel your subscription (for a short while) until you get back and save your money. There will be a laptop that can play FFXIV much more reasonably and at the same price in 1 or 2 years from now (or the same computer will be at 75% of its value by June).