Quilting refers to the technique of stitching a layer of insulation, such as cotton batting or polyester wadding, between two layers of fabric. The fabric can be of any size you wish as can the resultant quilt. The stitching used to hold the layers in place can be as plain or fancy as you like.
However I think you may mean 'patchwork'. Patchwork and quilting often get used in the same phrase and muddled with each other. Patchwork means as you know joining cloth pieces in a regular or random pattern to make a larger piece of fabric. Sometimes this patchwork fabric is then attached to a backing sheet of fabric with a layer of wadding in between the two, hence become a patchwork quilt.
You will find many online stores that sell 'fat quarters' for patchwork, and any of these will be a good starting point.
If you are learning, I would start small, with one multicoloured bundle of fat quarters, and make that into a cushion cover.
There are innumerable books and websites full of patchwork projects and the quantity of materials you need depends completely on what you want to make.