I'd actually recommend doing Palace of the Dead.
One to get familiar with gameplay again, two, it's a quick, cheap way of getting seals, and three... as soon as... what tuesday? It will be dropping ilvl 255 weapons when you advance far enough with it. Four - no gear requirement as it has it's own progression system. So you are in no danger of being locked out of it.
Doing the story and unlocking your dungeons as well will help get you enough lore to jump you into 230 gear, which, with the weapon, will push you over the necessary ilvl to get through Alex Normal, which will drop 250 gear. After that, you're just back to the weekly tome grind.
Anyways, welcome back. Kick back and have some fun. Keep in mind this is likely the last ilvl hike until Stormblood, so no rush for things.