The factor that best defines the professionality of your Web design company isn't how pretty a site they've created for you. It is how effectively your site converts visitors into customers.
A Web site is a tool. It is not the end result of working with a professional design company; it is the means to a greater end. That end result could be making contact with a potential client, getting someone to sign up for a newsletter, making a sale through an online store, generating followers within social media sites - the list goes on and on. The important thing is that the end result supports your business's objectives.