My only advice is to look at the common side effects, work out which method might suit you best, and then give it a try. Eg, if someone is forgetful a coil, implant or the injection might be best; otherwise the pill would be fine. As a very brief and general overview, here goes:
Combined pill: loads of different types; you might not suit the first one you try, but the majority of women will find one which suits them well; not suitable for women with a family history of clots/heart attacks/stroke, or for women with high blood pressure generally speaking; can expect 3-6 months of side effects inc mood swings, weight gain, breast tenderness, etc (these side effects settle within 6 months max with most women); can expect periods to become shorter and lighter; can run packets together if on certain types of pill (meaning you can skip periods if going on holiday etc); 24 hour window, so if you don’t take it exactly the same time every day, it doesn’t matter; fertility on average takes 6-18 months to return to normal once you stop taking it.
Mini-pill: progestogen only; typically stops periods completely; may experience irregular bleeding or spotting; suitable for women with a history of high blood pressure/heart attacks/strokes; can expect hormonal side effects for 3-6 months while your body adjusts; most only have a 3-hour window, so you need to be VERY good at taking it on time (Cerazette has a 12 hour window); fertility returns to normal almost straight away.
Implant: lasts 3 years; typically stops periods; can get irregular bleeding esp during the first 12 months; suitable for women with family history of strokes etc; don’t need to remember a pill every day; fertility returns to normal almost as soon as it’s removed; may experience bruising or infection where it’s inserted; can sometimes migrate and may need to be surgically removed in v small number of cases
Injection: very high dose of hormone, and so associated with numerous side effects; average weight gain is 2-3kg in the first year, and 1-2kg each subsequent year; lasts 14 weeks, so if you experience side effects, they will last at least this long; other side effects are as above (mood swings, etc; can also be associated with loss of libido and vaginal dryness); can affect fertility for up to 24 months after you stop having it; other risks inc small risk of osteoporosis in long-term users; usually stops periods completely, though some users get irregular bleeding.
Copper coil (IUD): hormone-free, so no hormonal side effects (mood swings, weight gain, etc); can make periods longer, heavier, and more painful. Fertility returns to normal as soon as it’s removed. Fitting can be uncomfortable (though not too bad IMPO); women who haven’t had children are at an increased risk of abdo/pelvic pain. Very very small risk of perforation of the womb and PID.
Mirena: contains small dose of hormone. The dose is tiny and delivered locally, so although you MIGHT get hormonal side effects, usually they aren’t too severe and don’t last long; usually stops periods; can again cause pelvic/abdo pain, and again thyere is a TINY risk of perforation of the uterus and PID. Fertility returns to normal once removed.
Condoms: much less effective: around 98% if used perfectly, otherwise around 92% (most people don’t use them properly). Can reduce spontaneity and sensation. I personally only use these as a barrier to protect against STDs; I would never use them on their own, or in a long-term relationship
Diaphragm: around 92% effective. Needs to be inserted well before sex so affects spotaneity; needs to be kept in after sex for some time to increase efficacy. I would not use this unless I didn’t mind falling pregnant.
Other methods inc the Nuva ring and contraceptive patch, which are similar to the combined pill in terms of side effects and so on; the nuva ring is worn in the vagina, the patch usually on an arm/on your bum; both are effective for 3 weeks, at which point most women have a 1 week break before applying a new one, but like the combined pill, you can use a new one straight away and skip the weeks break (and your period)