It depends a lot on you and your lifestyle. I'll try to cover the benefits and disadvantages of different things briefly:
Pill:
- must remember to take daily, same time of day
- won't be given if you are significantly overweight, may also affect your weight regardless of what it is currently
- may affect your mood as it's hormonal
- will be affected by things like antibiotics
- can be used back to back to skip/change periods if you want to avoid one when on holiday etc.
- non-invasive
(there are lots of types of pill available and some points might not apply to all)
Implant:
- hurts when put in (bit more than injection) and when replaced/removed
- "gross" to have something you can feel under your skin
- may affect your cycle (good: remove periods entirely, bad: potential for constant bleeding/unexpected periods)
- only needs to be replaced after 3 years, no need to remember anything on daily basis
- less affected by medicines than the pill
Coil:
- "very" invasive procedure, but not really that different to a smear I guess
- may affect your cycle (can make periods lighter or significantly heavier)
- can get stuck/moved and cause bleeding or other problems
- only needs to be replaced (I think) every 10 years, no need to remember things
- non-hormonal
Personally I use the implant, I'm on my second one having had it replaced before I went to Germany, and I absolutely rate it! I was intrigued by the procedure and watched them do it, but if you're squeamish you can take a friend/mum and just not look - it doesn't take too long. I've had maybe 4 bleeds since I had my first one, plus a lot of spotting towards the end of the first one's life, and I've not had any mood swings (I used to get them quite badly).
But I know people who have used the other methods and loved them, or hated them, and people who've used the implant and hated it. It may well be a question of what you think is most suitable to try first (I found my sister reacted to the implant exactly the same as me, so maybe close family members will give you an idea of whether there might be issues) and see how it goes. You might need to muddle around to find something that works properly for what you want.