Anyway to choose type of subdivide?

Is there a option that does a triangular subdivide instead of a rectangular one on a face?

CTRL+T in Edit mode ?

Not as far as I know. You can triangulate at any time though - edit mode, CTRL-T, as organic said. I just wanted to clarify that subdivide and triangulation are separate functions in blender. If you triangulate first, then subdivide, your tris will subdivide. Play with Ctrl-T.