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I frequently oil-paint with watercolor brushes. In fact, I would oil paint with a broom if I thought it would give me the result I wanted.
However, it was not always thus. For someone who dreaded school every day of the long years of secondary education, lest an unwitting infraction of an unwritten rule result in a trip to the principal's office, the categories in which paint brushes are typically arrayed in art supply inventories implied boundaries not to be breached.
While neither professionals nor serious hobbyists are likely to be hindered by such things, anyone new to the wide world of art supplies might assume that brush categories are part of some greater "right way" of doing things. And while it's true that in a mass-market-averaging-sort-of-way various brush categories are more or less suited to certain media and techniques, the bottom line (i.e., the greater "right way" of doing things) is simply a matter of "whatever works."
Buy in person
Even though painting is classified as a visual art, that classification focuses on the viewer. From the artist's standpoint -- at least the standpoint of this artist -- painting is a tactile art. And the paint brush is the tactile tool by which the artist is engaged.
I buy brushes on the basis of a tactile examination of the tool. I would like to be able to buy brushes on the Internet, but I have to grasp the brush, make strokes with it in the air, and thumb its bristles. A brush is the baton by which I conduct the orchestra of thoughts and feelings and substances that join in the music of my painting.
Every characteristic of a brush -- the way the contours of its handle balance weight and weightlessness when joined with hand and eye, the smoothness of the handle's finish, the thickness and responsiveness of its bristles, etc., etc. -- must meet in terms of touch so that the brush is both present and altogether absent, just as the hand becomes an invisible extension of mind and heart (invisible because it becomes one with them, disappearing in the achievement of their purpose).
Buy quality
Quality is best judged by experience with a style or brand of brush. Price sometimes indicates quality, but not always. Experiment with brands and styles, and don't be afraid to pay for the privilege.