Black pepper is most commonly used. I prefer to have whole peppercorns in a mill and grind them as needed. This ensures that the maximum flavour and fragrance is achieved. Preground or crushed pepper is great to use.
If you use white pepper, use it sparingly to start with, you can always add more. It is used in Asian cooking a fair amount.
Green peppercorns are traditionally used in a sauce for steak. You very rarely see them dried. You can buy them fresh from some Asian supermarkets or in brine. They are generally used whole and give a great peppery kick. Try adding a few to a hot and sour soup.
Pink peppercorns can occasionally be found too. They have a pungent and slightly sweet flavour. They are the berries of a rose like shrub (Baies), and are not true peppercorns. Try them crushed in dishes that you would perhaps use juniper berries in. Use sparingly.