Currently, there exists 4 Shops. All the shop offerings seems to change on a regular basis.
Here, you use Zenny to buy Consumable Items that you can use during combat.
Health items are guaranteed.
Rare Medal Shop
Here, you use Rare Medals to buy Reincarnation Cherubs, Metal Keys and Gold Bundles. Sometimes, you can buy Fusion materials for Units and Gears.
Battle Medal Shop
Here, you use Battle Medals to buy Units, Pixies and Gear, that are constantly changing. Special Event Units and Gears may also appear here.
One Sereine Recipe is guaranteed.
Here, you use Lazuli to buy Special Summon Tickets that guarantees 4-5 star unit, 5 star Pixies and Skill Dollies.