First thing a woman should consider is lactation because during the first month of breast-feeding, women should avoid using any hormonal contraceptive that contains estrogen because the estrogen could reduce milk supply.
On the other hand progesterone-based contraceptives and contraceptives, like condoms, are fine to use. Additionally, often breast-feeding suppresses ovulation, which is probably a good reason why birth control pills are not recommendable during first 6 months while breastfeeding. However, best option would be to check with your doctor to be sure.
Women who have problems with blood cloths or a diagnosis of deep vein thrombosis should abstain from any hormonal products with estrogen, since this hormone can increase the risk of clots. Again, progesterone-only contraceptives, such as Depo-Provera shot or the progesterone-releasing Mirena IUD, are safe to use.
Breast cancer survivors should use any hormonal methods of contraception. Condoms or a diaphragm are bets options available, while suffers of ovarian are safe to use all methods and those with cervical cancer should avoid using IUDs, since insertion can irritate the cervical lining.
If you are suffering from uterine fibroids, all methods of contraception are safe to use.
Women with heart problems or high blood pressure should on the other hand avoid estrogen-containing contraceptives because they could increase heart problems in the future.
If a woman has diabetes it is usually safe to use any contraceptive method. However, if there are kidney problems, vascular disease, vision decline, or nerve disorders involved estrogen contraceptives should be avoided.
Women who underwent radical procedure that had shortened the length of the small intestine should avoid oral contraceptives. Women who suffer from rheumatoid arthritis should avoid using Depo-Provera, since the drugs decreases bone density. On the other hand women who suffer from inflammatory bowel disease should avoid using estrogen-containing contraceptives, while women who have undergone successful transplants can generally use any method safely. Only those with complications should avoid using estrogen-containing contraceptives and should also avoid using an IUD.