Yeah this is essentially a shopping cart. The database will depend on the machine hosting it, but any database can work. I would go with one that supports referential integrity (keys). The idea is that you are going to have three tables. One will be for the user's account and has an account ID that is assigned to them when they signup (this can be a auto_incrementing primary key). A table that has all the items you have for the site which each item has their own item id and another which will keep a list of IDs for items in their wishlist. You don't have to store much more information in the wishlist table than the items unique key id because then you could use that ID in a query to pull the items information as needed.
CODE
User
-----------------
UserID
Name
Email
Password
Items
-----------------
ItemID
Itemname
Quantity
Price
User_Wishlist
-----------------
ID
UserID
ItemID
As you can see the user_wishlist table has a link to the userID and a link to ItemID. This table can have multiple ItemIDs for each userID and will look like...
CODE
1,3,10
2,3,22
3,4,10
This above says that wishlist for user 3 has two items, item 10 and item 22. User 4 has item 10 only. I hope that part makes some sense.
I was not able to find any article that gave you the simple relationship here because it is pretty elementary database design but you can look at shopping cart table design or the classic "order/item" table design which fits very close with this. Just replace order with the idea of a wishlist.
I hope this information helps.