It is the pervading law of all things organic and inorganic,
Of all things physical and metaphysical,
Of all things human and all things super-human,
Of all true manifestations of the head,
Of the heart, of the soul,
That the life is recognizable in its expression,
That form ever follows function. This is the law.
-- Louis Sullivan, Architect, 1896

I have noticed that most people, when pondering a new website, begin by looking at ready made templates, other people's websites (many of which were made from ready-made templates), settle on one with their own unique modifications (such as logo), and then try to fit what they want to do into that pre-defined format.

I suggest that the opposite approach may prove more fruitful.  Start with your data and your purpose.  What do you want to do?  Share information?  Do you have a large database of inventory or information you wish to present in a friendly way?  Do you wish to write often?  Do you have a lot of pictures you want to show?  What is your main intent?  Once you have defined what it is you want to do, think about how your information could be best presented.   You might need dynamically generated charts and graphs based on your data, or you might need a shopping system, or a blog format.

After you have defined your purpose, and decided on what you want to present, how, you can accessorize and emphasize with a coherent design.  It is very important for the programmer, who makes things go, work very closely with the designer, who makes things look right.