It sounds like you may be having connection issues? The game seems very slow-paced when you start because of the 2 second GCD and easy combat. As the game progresses though (and depending on the job you pick) there are many things to do inbetween the GCD and fights get more hectic.

It sounds like you may just be having a latency issue if you feel your movement is stilted and buggy. Try a wired connection if you aren't on one and also test your latency/ping against the DataCenter/Server you are on to see if there are missing packets. Some people use gaming VPN clients like WTFast that help smooth this over.

The last thing I wanted to mention is the race you play. While it does sound like your problem is technical, all the races have their own feel to movement and animations. Some I can't stand and others I love. Give them all a shot!