A popular alternative to a starting chain and a row of single crochet is the foundation single crochet (fsc). This is helpful in projects where you know how long or wide you want your first row of crochet to be, but aren't sure how many stitches you need to start with, since you can just add fsc stitches until you reach your desired length. This stitch creates a fairly stretchy foundation, which you may want if you are crocheting a garment or other item where a stretchy foundation would be preferred.
Many people like the foundation single crochet because it creates the chain and the first row of single crochet stitches all in one, so you don't have to do separate steps. This is particularly useful for graphghans or mosaic crochet projects.
Below is a video tutorial that demonstrates how to create the foundation single crochet stitch.