FFXIV does not play well with others..as in other programs. Turn off any and all programs running in the background on your PC, esp (but not limited to) all programs that access the Internet.

Any program that "checks the internet for updates" is usually the culprit. Some will be on your taskbar but unfortunately many are hidden. Check your Task Manager and click on the Applications tab. You will possibly be horrified at how many programs are running and slowing down your whole system (not to mention crashing your game).

Turn off/exit/disable everything that doesn't kill your Internet Connection is my advice, but be careful and good luck.