Our two biggest needs were bookshelves (can't stop buying books!) and a place for art/craft supplies. We filled a wall in the den with bookshelves, and that took care of the book issue. For craft supplies, we had a built-in pantry right off the breakfast room. I dedicated 1/2 of the pantry to craft supplies which the kids were free to use at the breakfast table whenever they felt like it--as long as we weren't eating at the time.
Our actual homeschooling years occurred when our kids were older--after these spaces I've described were created. During the homeschooling years, we never had a specific place for learning. By that point, we felt like one of the problems with school is that learning is artificially restricted to certain time periods and spaces. Regarding time, why cut off a subject with a bell when a child is still enthralled with it? As for spaces, other than controlling clutter and/or possible spills, you can be pretty liberal with space. After all, learning can take place anywhere.