During the "eclipse of Darwinism," when natural selection fell out of favor (between Darwin's death and the modern synthesis), the two major competing groups of note were the Biometricians and the Mendelians.

The Biometrician school was founded in sorts by Francis Galton and continued by the likes of Karl Pearson and W.F. Weldon. They were essentially statisticians approaching biology. Their hereditary model was essentially a hard, blended one — children are 1/2 of each of their parents, and development (e.g. environment) mattered little. They were also saltationists of a sort — they believed that real evolutionary change happened in "jumps" and was not gradual. They did not have a good explanation for where those jumps came from, biologically. They believed that natural selection did work in the sense that it created variation within types, but they didn't believe it created significant changes between types. (This is similar to a common Creationist argument these days — you can modify dogs all you want through artificial selection, but you can't make them cats.) In retrospect it can be hard to picture where they really diverged from Darwin but this is partially because we've assimilated so much of the modern synthesis in our reading of Darwin. They saw stark divisions in both their theories and their methods (very hard statistics).

The other major group, starting around the turn of the 20th century, were the Mendelians. (You could call them neo-Mendelians, if you wanted, since they were not really followers of Mendel per se.) William Bateson was the most prominent of these during his day. Basically they argued for saltationism but one that worked by means of Mendelian unit characters. So where the Biometricians saw smooth heredity, the Mendelians saw big clunky jumps. This coupled with things like De Vrie's Mutation theory which argued that big changes in evolution came not from selection but from random major changes that occurred.

There were a few hardcore Darwinians during this time, like August Weisman, who fashioned himself a neo-Darwinian. It should be noted that Weisman and this sort picked and chose what varieties of Darwinism to support — Darwin himself was a little wishy-washy when it came to his model of heredity in his later works.

All of these sound awfully similar to parts of the modern synthesis — which is basically what the modern synthesis is, taking the best parts of all of these approaches and coupling them up with natural selection to make it much more robust. When we speak of the eclipse of Darwinism, we are in some ways talking about very fine line debates about the nature of heredity and the nature of speciation, and whether natural selection alone can accommodate entirely new developments. The parties in question saw very stark differences between themselves, and stark differences between their views and Darwin's, but in retrospect they seem to agree on quite a lot.

As for your bonus question — Darwin himself was extremely frustrated with the fact that natural selection got ignored by many and the differences between him and others like Lamarck or Robert Chambers (Vestiges of the Natural History of Creation) were often unappreciated or underplayed. I think we can say that there was a popular reception of Darwin and a learned one. The popular one did not really appreciate the subtleties and what mattered was that Darwin gave an extremely respectable voice to something that had previously been relegated to the area of salacious popular science (e.g. Chambers). The learned one did at times appreciate the distinctions and engaged in the very esoteric debates over modes of selection (e.g. Darwin vs. Wallace on sexual selection, Darwin vs. Galton on gemmules). The problem that the learned scholars had with natural selection is that it seemed inadequate to the task, in part because the time scales of the Earth were not properly appreciated (it is much older than they realized) and the speed of evolution not correctly understood (it can operate much faster than they realized).

For further reading, Peter Bowler's work is pretty definitive (I am partial to his The Mendelian Revolution, but his Evolution: The History of an Idea covers a lot of this ground too, including a chapter on the eclipse of Darwinism), and Donald MacKenzie's Statistics in Britain, 1865-1930 really does a lot with the Biometrician vs. Mendelian debate. On Darwin's immediate reception, I am a fan of the biographies by Janet Browne.