To make the best decision for yourself, you really need to discuss the pros and cons of each with your doctor. The male and female condoms and the contraceptive sponge have the great advantage of being available without a prescription. The diaphragm and cervical cap must be fitted by a professional and purchased with a prescription.
Some men object to using condoms.
The sponge and the cap are less effective in preventing pregnancy in women who have had children already. The diaphragm, especially, also increases the likelihood that a women will get a urinary tract infection following intercourse. In short, these methods can be cheap, can be used by a woman without her partner's knowledge, and involve no hormones. However, they are the least effective contraceptives around, mostly because people tend to skip using them from time to time or don't insert them correctly. Since they are hormones, they may cause side effects.