Midsize animal hospital, pet clinic....call it what you will (it's all the same)
This type of veterinary facility is perfect for almost everyone, whether they know it or not! Usually there are three to four doctors on staff. They are usually equipped with all they need to help diagnose and treat your pet's ailment.
And they have enough doctors that they can serve you in a timely, efficient manner. By that I mean one or two doctors may be seeing clients, while another may be doing a dentistry or surgery while the fourth may be having his day off (just kidding). The point being (other than I personally prefer 'mom and pop' or 'mid-size practices') is that clients waiting for routine checkups, whatever, will not have their whole day messed up because an emergency walked in the door.
These doctors have probably been schooled along with the best vets working in emergency and specialty hospitals, but opted to practice where their love of animals and people does not get clouded by a huge overhead.
They can handle most problems yet will refer 'out' if they deem it necessary.