Let the user move the UI pieces around the page at
will. Save the layout for the next time the user resumes
using the software, especially if it's an important part
of his daily life.
Depending upon the design you've chosen, you may want to
give the user freedom to place these pieces anywhere at all,
even if they overlap. Or you may want a prescribed layout
grid with "slots" where pieces can be dropped -- this
lets the page maintain alignment (and some sense of
dignity!) without making the user spend too much time
fiddling with windows.
If the movable panels react to mouse clicks or mouse drags,
such as for text selection, consider putting a "handle"
on each piece that the user can grab to move the piece around.
Titlebars are good for this. In fact, if you put an "X" on
the handle, some users will conclude that that is how they get rid
of a piece entirely. (If you implement this, of course, offer
a way to recreate the pieces that are gone!)
Your users might appreciate a "Revert to Default Layout" action
somewhere on the UI, if they get completely tangled up and
just want to start over. When you usability-test Movable Panels,
watch especially for accidental panel moves -- a user who
unintentionally drags a panel into an odd place may not know
immediately what he did or how to undo it.