I saved some registry keys to a file, these:
HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\Main - Window Placement info
HKEY_CURRENT_USER\Software\Microsoft\Internet Explorer\Document Windows
width, height, x, y, and it looks like there's a Maximized option there. Trying that....
Edit: The Maximized option under Document Windows doesn't seem to do anything.
But anyway, with those settings in a registry file, I just close IE (can't apply new settings while it's running), and double click a shortcut to that exported registry file. This merges those settings into the registry, and IE opens how I want it.
To define a window size, adjust the IE window to how you want it (it can not open maximized; I've read that IE can't do this), hold down Shift, and close the window. IE will open new windows in that same size now.