There are four basic areas in your Home, and each one has stats which can be modified by placing furniture in them. Some furniture can go in any non-Yard area and can trigger various character events.
Knowledge - Unlocks recipes for synthesis
Clerk - Maximum number of clerks in the store
Stock - Maximum number of any given item that can be sold
Sales - Affects how many items customers will buy
Attract - The chance a customer will visit Wil's store
Prices - Modifier to the cost of items sold
Tools - Amount of materials needed for synthesis
Formula: Final material cost = Original material cost x [1 - (Tools / 100)], rounded up (e.g., a Tools value of 24 affecting an original material cost of 4 produces a final material cost of 3.04, rounded up to 4)
Exceptions: For every 33 P, recipes that require 3 of an ingredient will need 1 less of that ingredient (e.g., 2 Stone for Good Stone instead of 3). Minimal cost is 1 for each material.
Skill - Synthesis experience gained
Mutate - Chance that something unexpected will occur
Sense - Unlocks recipes for synthesis
Furniture placed in the yard will also generate items for harvest over time and may lead to character events
To assign your characters as shop keepers, go to your home and enter the Party Menu. Select the character and click the "Manage Shop" button below the character select portion. The character will no longer be allowed to enter a dungeon so long as they are managing the shop. A character's ability to sell items in the shop is dependent on the "Serv" stat. Yuela has the lowest with a value of 4; however, equiping her with her strongest weapon (Kitchen Knife) and strongest Character specific accessory (Eastern Pin) gives her +30 to Service. If you don't put anyone in, the default shop keeper will act as your salesperson.