When I was first married, my husband would never have described me as "crafty". Over the years, my eyes have been opened to scrapbooking, card making, hair accessories, and household projects. For the first several years as my crafting was expanding, what did I use to hold my craft items?
A suitcase! I was given a small suitcase on wheels as a Christmas gift from an employer, and it quickly became my craft "container". A suitcase can work really well for a moderate or beginning crafter because it can be stored vertically or horizontally, and it is easy to transport.
Look around your home, and find many creative ways to contain your crafting treasures!