I consulted my father on this one, as he is a professional woodworker.
He was very suprised to hear that you are planning on painting the
furniture and at the same time are concerned about the wood grain;
painting will cover up any visible grain. Pigmented wood STAIN,
however, perhaps followed by a clear finish coat, is the most logical
choice, and I get the feeling this is what you were speaking of in
So, for this use and of those two options, you will want to use Beech
wood, because it has a much less evident grain, and will result in the
smoother surface you described.
I hope this answered your question! If necessary, please request a
question clarification, especially before rating this answer. Thank
you for bringing your question to us!
PS- If you ARE actually planning on painting these pieces, keep in
mind that you will not see the grain at all. If this is the case,
there are much better woods to use than beech or oak, such as maple,
simply because they are harder and will be more sturdy.