Following up on the Wikiart dataset, I finally downloaded it and ran the standard fastai lesson 1 process on it. And guess what, I got 60% accuracy predicting the exact right style. I find that very impressive. My attention was drawn to this dataset after reading the paper The Shape of Art History in the Eyes of the Machine and as far as I can see, their best accuracy was 60% as well. (Of course the paper goes much further than just doing classification, but I still find this very impressive).
One lesson I took away: Sometimes you might need to filter out corrupt images, as my learner seemed to crash on .fit_one_cycle when it encountered strange, truncated images.