The shops can be accessed from the main menu, in the red icon (商店街). There you have three major NPCs to visit: Cork, on the Trade Shop; Polka on the Forge and Kanna on the Architecture Shop.
For further information, visit the NPC function's specific pages.
Here you can create and manage your weapons.
For more information, look at the Weapons page.
Since you have a town and two personal rooms, some buildings and furniture are necessary. In this shop you can expand the amount in storage (for both) however only buy movables for your rooms. The construction are on the "Town View".
For more information, look at the Buildings or Furniture pages.