Hey Chris,
Like most things I would have to say, it depends.
I would not hesitate to print your typical digital P&S at 11 x 14. If the image is not particularly sharp, that may be too big. Since the print would be on a rough surface, you could go bigger. Some images look better very sharp, others look good soft. So I don't think there is any exact answer.
Prior to buying a photo printer I used Costco for general printing and found the quality to be just fine. I even had a few of what I considered at the time large prints ( 11 x 14 ) done by them and they were good and inexpensive. Many moons ago when I submitted some photos to the county fair I used Bayphoto. A locally owned chain that did quality work for both analog & digital and still do. You probably have a similar shop around your neck of the woods.