Yes right here:
Become the Warrior of Light, and fight to deliver the realm from certain destruction. Play the Free Trial up to level 70 for FREE with no restriction on playtime!
freetrial.finalfantasyxiv.com
it's absurdly long for a trial. you can reach level 60, and play through base game and great first expansion. You'll likely know you like the game before then, but the first expansion, heavensward, is considered one of the best final fantasy stories.
If you intend to buy the game, you can follow some one's link to be buddies and give them a reward. not sure if it stacks with trial or if a trial goer can use a buddy code to migrate to full subscriber. some one let me know if it works.
II. What class / race should i play?
Race literally doesn't matter. play with the styles and emotes and play something you like. There are plenty of weeby races, but others are standard fantasy fare.
In ff14 you can change class at will once you unlock them. each class has their own level which rises independently (for combat, gathering, and crafting classes).
They are some what balanced with deviations on how they play, some are button mashier than others, some are one trick ponies, but they all do roughly similar tanking, healing , or dpsing. Some may make you want to kill yourself, so try lots of them.
it's worth noting that Healers followed by tanks followed by dps is the queue speed. so some people level a tank/healer for doing roulettes, and then level a DPS in the MSQ.
This wiki page has a great chart toward the top showing you what level various classes unlock.
ffxiv.consolegameswiki.com
Each expansion added some classes and they start 'higher level' than base.
this video spends like 45 second giving you a raw run down of each class, pretty accurate: