The main reason there's a difference in reliability between the combined pill and a progesterone-only 'mini pill' is the way you have to take most of the latter types within a couple of hours of the same time every day. Not everyone can do that and failure can lead to ovulation and, if you have sex at the right / wrong time, pregnancy.
If you can do that, you're primarily looking at things like interactions with other drugs, including 'natural' remedies like St John's Wort, or vomiting within an hour or so of taking it and then not relying on other contraception for a week.
Even having a sterilisation op doesn't come with a 100% guarantee. The nearest any single method comes to that is the implant and if you're fine with progesterone-based contraception, you could look at that.