The new profile layouts are quite complex so the best thing is to just look for yourself and go by trial and error. It was quite a chore when I came to editing it for the first time so be prepared for a long night when you start
Anyway, all the profile page consists of memberinfo templates, there is the main MEMBERINFO template which contains the main structure & layout of the profile page. It does have a few comments to say where things are so you might be able to use those. Each of the little sections on the Profile page are knowns as "Blocks".
I found it quite difficult to edit the tab menu as it consists of a mix of HTML Javascript and CSS so I gave up in the end.
For Calricdal, to edit the order of the you will need to change the order of the "$block_data" variables (I think thats what they are called) and place the visitor message block lower down in the list. This is all in the memberinfo template, I think.