i work for a company who develops websites and i have the great job of designing and developing the sites that we produce.
my of tackling it is to design the site first then add the functionality to it later. as for changing the design all the time this is going to happen i feel with any site that you under take as you will design something one way come in the next day after a brain wave the night before and change sections of it.
this is how i work but i feel it is probably down to the person who has the task in front of them as you only know yourself what you are most comfortable doing.
for instance if you find the coding harder then you may leave this to the end and vise versa it just depends on what which side of things you are better suited to.