I think most of this post is pretty bad advice. Emachines are pretty much cookie cutter computers and if you go out and buy a video card, it may or may not be able to handle it, or even actually fit in the case. Then you go and try to find a power supply, but it won't fit in the case or doesn't have the right adapters for your video card. IMO a better bet is taking the parts that will fit in a new rig. Hard drive, maybe ram, fans, cdrom, and then rebuilding.
If you don't know someone that can help you build, then try a local computer store.
Finally, another point is, wait for the game to come out. See how it looks and plays. If it is unplayable, wait to see if there are updates to ffxiv and drivers for your hardware a few weeks after release. If you are ok with waiting, don't even buy the game until it has a few months under its wings. Most debut games have a lot of let's just say "figuring out time" before drivers and hardware agree with each other in a mass scale.
First, retail computers are just a bunch of parts that you're paying someone else to assemble for you anyway, only you have less input into which parts they use. An eMachines computer isn't "an eMachines computer"; it's a motherboard from one company, a hard drive from another company, a power supply from another company... all put in an eMachines case with Windows (usually) installed on it. eMachines is no worse than Dell is no worse than HP is no worse than anything else, because the only difference is the service/support and the case.
That said, I do always advise people who are serious about gaming to build their own rigs. If you want a quality gaming rig, most retail outlets will charge $1000-1200ish for them, whereas you could build them for $800-1000. If you're only using the computer for general web/word/email, then a retail model is the better buy, but if you're planning to spend 1k+ for a shelf model, building it will give you more control over your parts (allowing you to pick better brands instead of whatever the cheapest they could find was) and a lower cost, or higher performance for the same cost.
As for waiting, I would advise this if people are hesitant, but chances are the result of waiting will be that if they play the game and don't like it, they will feel pressured to run out and buy the first thing they see, potentially making poor purchasing decisions, because they want to play the game quickly. This holds especially true for people who got the CE.