Some details: First off, this is all PC/Mac version only, and is for downloading the game directly from Square, not Steam or anything. If you have Amazon Prime, you can connect that to your Twitch account for free, which gives you certain deals. Right now, one of the deals is Final Fantasy XIV: A Realm Reborn base game for free, with 30 days of subscription. That deal lasts until May 3. Now there's this Golden Week deal from Square-Enix themselves, where you can get the first major FFXIV expansion pack, Heavensward, for free - that deal lasts through June 27.
Heavenward extends the story and game quite a bit, basically doubling the size of the game and adding flying mounts. The Heavensward expansion is better than the base game, as the story flows better, most side quests aren't as grindy, dungeons are better, etc. Note that as Heavensward is an extension to the story, you can't actually access most of its content until you've finished the main game "Realm Reborn" story, which takes you through level 50 (similary, you can't access the newer Stormblood expansion content until you've completed Heavensward, and the next expansion "Shadowbringers" requires finishing Stormblood). They do sell an object (for cash) to bypass earlier story bits, but I wouldn't recommend it for new players, it's best to play through the story to learn the characters and their situations, and a better way to learn how to play your character classes. Square has streamlined getting through the earlier parts of the game, making some dungeons/bosses easier and making sure you always have necessary armor and weapons and whatnot without extra grinding.