When you first begin the game and create a new character, one of the options will be to choose your character's family profession. Several are extremely helpful over the course of the game. Each character created on your memory card with a unique profession will occupy a new house in your home town, Tipa. So even if you plan on playing with just one character, its best to create several with a variety of professions so you can utilize them all.
Each profession has a production level, which corresponds directly to your relationship with your father in the game. The major way of increasing your family's liking of you is to reply favorably with the letters that you receive after gathering myrrh drops at each location. You must pick polite and appropriate responses to your family letters and always send something home. You get bonus points with your father if you send something home that relates to his profession: ex. sending a seed home to a farmer. As the production level goes up in your family profession, the more items or accessories are available to you in that profession, furthermore you get better discounts when you shop at your family's Merchant, Blacksmith or Tailor professions. To summarize family liking and discounts, here is a quick chart:
The alchemist studies nature and the very fabric of the world. Through this profession, the alchemist father can create new items. Starting with year two of your caravan, the father will give you one new scroll each year. What scroll he'll give you depends on his production level. Almost anything is good to send home to an alchemist father through your letters.
The blacksmith is one of the most valuable parents in the game. You can always come back home to Tipa and bring materials and scrolls to forge weapons and armors that you cannot forge anywhere else in the game. As your father's production level rises, he'll be able to make more and more items. Thankfully, other characters can benefit from his production level.
Farmers are not the best of professions to have in the long run. Sure, its easy to please a farmer family by sending home bundles of seeds, but the most you will get out of them is Bannock Breads (if you send home Wheat Seeds). If upon receiving Bannock Bread, you'll receive bundles of wheat two years later. Other than those two minor bonuses, there isn't much to the farmer profession.
The fisherman profession isn't a very useful one. Every year you come back to Tipa, your father will give you a random amount of Fish to eat. The amount you receive varies according to how well your relations are with your family and your responses to your father's fishing questions. Other than the Fish bonus, there isn't really anything special about the Fisherman profession.
The merchant may not have many items at first, but once his production level rises, you get better discounts and access to better materials and items to buy. You can even sell items at a marked up price to your father depending on your relationship with him. Other players can use your father's expanded inventory during the game, but they will not receive discounts.
The miller father is similar to the farmer in that if you send home Wheat Seeds, you will start receiving Bannock Bread, and after two years you'll receive Bags of Flour. Other than those two minor bonuses, there's isn't much else to the profession. Seeds are your best bet to make this family happy.
The rancher father is similar to the fisherman, but instead of fish, you receive Meat slices. The amount of slices depends on your relationship with your father. After three years, you will start receiving bottles of milk. Sending a cow home from the Fields of Fum will score major bonus points with your father. Other than those points noted, that's all there is to the profession.
What the blacksmith does to weapons and armor, the tailor does for accessories. You must bring your tailor father materials and scrolls to craft an accessory. Like other professions, the amount of things he can craft depends on his production level. Other players can use his expanded services as well, but without the discounts.