Based on the things you don't want, you're limited to barrier methods - condoms, diaphragms, etc.
I personally did A LOT of reasearch when I was deciding on a BC option and I finally decided on mirena. Now, while it is hormonal and it did stop my periods (which I have been oh, so thankful for) - I don't ever have to think about it (it's good for 5 years), I have no cramps (I used to have horrible cramping monthly), it's low-dose hormones so I have not had any hormonal side-effects: gaining weight, mood swings, etc. Now, I know I am just one person, but I have talked with other moms who love this BC option too.
My husband and I had always used a barrier method before now with success, but after the birth of our second we really didn't want to take a chance at an unplanned pregnancy so we decided to beef up the BC and have been pleased.
I hope this helps a little. Here is a good website with just plan information about the different methods of BC - http://www.4woman.gov/faq/birthcont.htm#two