The pipe Merry gave Gimli in the ruins of Isengard was a small pipe, with a wide, flattened bowl. Not a churchwarden. The pipe Bilbo was smoking in the beginning of the Hobbit is described thus:
'By some curious chance one morning long ago in the quiet of the world, when there was less noise and more green, and the hobbits were still numerous and prosperous, and Bilbo Baggins was standing at his door after breakfast smoking an enormous long wooden pipe that reached nearly down to his woolly toes (neatly brushed) - Gandalf came by.'
When a guy named Valentine Erofeev wrote to Tolkien asking about the flavors of tobacco and shapes of pipes in the books, he received the following reply:
Dear M. Erofeev,
I hope not to offend you by answering the following. I think that the prologue says enough about Hobbits and their art of pipe-smoking. I do know people want more - but I think that covering the story in mysteries is a good thing, if not a necessery one. It also helps to replicate real history.
Regarding the taste, I'm inclined to answer that I do not know myself. The hobbit leaves surely made for very good flavoured pipe-weed (I would not say brand, as there's no question about commercial products here) but I've not given much thought to that until now - or if I did, my old memory is failling me somewhat. However, I do imagine that most pipes were primarily simple in design. Their shape would look similar to the the large half bent Billiard or Dublin shapes, but often much more long-stemmed.
Regarding the material, I think that Hobbits, if they could not grow suitable briar in the hills, would use hardwood like beech or oak - or perhaps even a type of wood I do not know about. These are details that, when writing, do not come to mind and that must be thought out later, if at all. I must admit I'm always hard put to give out so many of them, and in the end I often favour giving only a partial answer, lest the flavour of authenticity I try to give the story completely disappears. Indeed, I see my job primarily as that of a translator, not an encyclopedist!
My sincere greetings to a fellow pipe smoker,
J.R.R.T.