FFXIV is very very demanding. Only top-of-the-line systems run it at max settings without major problems. There are a couple of things you can do: turn off Ambient Occlusion, disable/lower shadows, run in Fullscreen mode (don't accidentally Alt+Tab), lower your drawing quality (though not too much or it gets too grainy to play). On the plus side, 2.0's new graphic engine (yes, they're writing a brand new one for it), should let you reduce quality and increase framerate more gracefully.

Hm...I'm going to guess you started in Limsa Lominsa or Gridania. Nobody lives there because the population is too low for the markets to get any use. Everyone is in Ul'dah. To leave Gridania, hit M to bring up your map and walk down the paths in the bottom-right or bottom-left corners of the town. To leave Limsa Lominsa, bring up your map and see if you're in the upper or lower docks. If you're in the Upper Docks, head to the inn in the middle of town (big round room) and take the stairs down to the first level. If you exit the first level heading east you'll run down a loooong bridge that leads to the region of La Noscea. Once out of town, bring up your Journal on the Main Menu and select the quest. If you click the map button it will show you where to do. All of the starter (L1-9) camps are very close to their respective cities, so you should be good from there.

I use a keyboard mostly, but use a mouse for precision targeting. I find that I play much more responsively with a keyboard, but others swear by a controller. I'd try both and see which you prefer.