Welcome back! I encourage you to keep the same character but start a new class. If you played at the 2010 launch, you'll need to play through the first ten levels as the class you are first. If you played at the 2013 launch, then you should have already unlocked the ability to start new classes by going to the corresponding guilds.

To answer your question about ways to transfer items to an alt, you either need someone you trust to trade the items or control of a free company of high enough rank to have access to the company chest.

As for guidance on where to go at what level, there's no shortage of such guides; just do a Google search and pick one. =)

As for job recommendations, just try what feels right; it's easy to switch among them. Personally, I'd recommend DPS if you feel no particular urge to heal.