In that price range finding a prebuilt ,much less with a monitor, that can play games is NOT going to happen.
Especially since FF14 hands a big ole bag of graphical rape to most machines.
I'm going to, of course, say build your own. Now ANYONE can build their own before you say you can't read into this -> http://www.pcityourself.com/
Building one is very straightforward and MUCH MUCH CHEAPER!!!! and we will gladly help you!
If you are open to building your own,
I think that either we can find something without a new monitor for now and you can save up for one. OR We can try a whole build in that budget but it'll be VERY limited in gaming power.
All in all I think some money needs to be saved.