It's always a good idea to hone in on several things before you start your search. First, what is the purpose/intent of the project? Is it for curtain panels, or to recover a chair? Is it for a few accent pillows, or all the bedding on a king-sized bed? What type of room? (formal living room, relaxed playroom for kids) These factors will help to influence how you go about choosing the fabric. There are thicker fabrics, with a high synthetic fabric ratio, which are great for re-upholstery. Then there are the washable fabrics and linens, which are better suited for bedding and removable pillow covers.
We also ask our clients what colors they are drawn towards, and what types of patterns (paisley, stripes, damask) they generally don't like. Of course, you also need to work with other existing elements in a room in most cases.
As an example, we were asked to find an updated but slightly formal fabric for roman shades for a bedroom, in blue. That meant that we were looking for a fabric that's not too heavy, with enough lightness that it will drape well as a shade, knowing the lining fabric needs to be considered. Here's the results from our initial fabric hunt: