Wheel sizes -- pros and cons

[alga]

What are the pros and cons of different wheel sizes? I know for a fact that smaller wheels with higher tyre sidewalls are lighter (my daily Civic's winter stamped steel wheels with 175/70R13 tyres weigh 9 kg each, whereas my summer 195/50R15 alloys weigh about 16 kg each!) Is that why Caterham uses 13" wheels? What are the benefits of bigger rims with lower tyres (except for looks)? As for cons, obviously they make the ride harsher.

On a related note, what about tyre widths? What does extra width give? School physics suggests that the friction is proportional to the force, so when the contact patch gets bigger, the pressure on it decreases, and the friction stays the same. This simple model misses something, as wider tyres usually have more grip. Any ideas?

What do you think are ideal wheel size and tyre width for a sevenesque roadster?