I was really happy with all of the different options and I would definately do it again. In fact, I plan on using the logo now and entering a business card design contest. My only complaint is that it was too hard to choose because of all of the amazing designs.
I really like a paw print as part of the design. Simple is best but still with a bit of interest. The clinic colours are the colours of the park: sky blue, grass/lime green, and with dark blue accents. I pictured the logo with Bickford Park, above the words ANIMAL HOSPITAL.