Like Geordie, I agree that Kocher (also my first eye-opener to the possibility of excellent Tolkien criticism) continues to age extremely well. And after that, yes, Tom Shippey is the dean of contemporary Tolkien critics; either book or both, dive in - I personally have a hard time telling them apart because his style is so distinctive. It is true that his lens is almost unrelentingly the historical-language aspect of Tolkien's writing, but you couldn't have a better introduction to the world of Tolkien as Tolkien himself primarily saw it.
Brian Rosebury: yes, indeed. Seek him out! The later edition of his slim but powerful book, Tolkien: A Cultural Phenomenon, is an update of the first edition, so don't bother with the earlier one. Begging Geordie's pardon, but you can get a used paperback copy from Amazon's resellers for a few dollars. Rosebury, as per his title, approaches Tolkien from the cultural studies angle. That sounds "softer" than medievalism, but he is unrelentingly rigorous and cuts a wide swathe through much of the modern blather about JRRT.
Now, that is a lot to read, but I will also direct you to the three (shorter) books of Prof. Verlyn Flieger, starting with Splintered Light, following with A Question of Time and Interrupted Music. Flieger is an interesting counterpoint to Shippey. She shares his medievalist outlook, but she is ... I don't know ... more flashy, or brilliant, or focused, or something. Maybe it's just that her books take on a single important theme in Tolkien, and stick with it; while Shippey is more encyclopedic. Why don't you read them all and get back to us?
Also: John Garth, Janet Croft, and William Green are other authors whose Tolkien books I have enjoyed. There are many more that I don't mean to slight by omission here. You might consider getting a subscription to, and back copies of, the hardbound scholarly journal Tolkien Studies (U. of W. Va. Press) for a good annual overview of the field; and although I am not familiar with it, the older and harder-to-find journal Mythlore has long had a reputation for publishing excellent critical articles on Tolkien, along with some that are not so excellent.