Family and Professions:

Each character's family has one family trade.  If you do not have a profession available
to you, you will have general access to it in your home town, although at a higher price.
Furthermore, your family's progress will generally follow your own.

Alchemist - Fuses Magicite together, produces 1-shot magic items, and works with crystals
Blacksmith - Creates armor, weapons, and metalworking
Crafters - Creates miscellaneous magic items, woodworking, and shoes.
Farmer/Miller - Creates outposts and miasma resistance food
Fisherman - Access to quality ships and seafaring expertise.  Also gets fish.
Merchant - Cheaper prices for buying, better prices for selling.  Can get goods not
   available from others.
Rancher - Access to quality (and sometimes exotic) mounts.  Also gets milk and meat.
Tailor - Crafts clothing and accessories, as well as non-metal armor.

Keep in mind that family functions are available to everyone, although the child of such
a family will (usually) get the best prices.  In addition, you should send home goods that
have to do with your family trade.

To start with (and every year thereafter), the family will usually give their son/daughter
 a present to help them in their journeys.  Listed below are the year 1 bonuses.

Alchemist - One level 1 base magicite of their choice or an Alchemist's Lab +4 (+4 to
  alchemy checks).
Blacksmith - +1 attack, damage, or DR to one piece of equipment (temporary until next
  year)
Crafters - +5 boots of jumping, +5 artisan's tools (Grants a +5 bonus to one type of
  craft skill, also operates as tools for any other craft skill), or a Spyglass.
Farmer/Miller - Traveler's food pack (Supplies food for one person indefinitely, of that
  person's choice and flavor).
Fisherman - +5 rope (+5 to use rope checks), Net of Capture (Works as a normal net,
  except it cannot be burst), or a Sailor's Cap +5 (+5 to Profession: Sailor checks)
Merchant - 300 extra starting gil.  This gil can be spent before the start of the game.
Rancher - A Chocobo mount with leather barding and all the supplies needed to ride and
  maintain it.
Tailor - Traveler's Cloak (Protects the wearer from most temperature changes).