Regarding birth control -
Invasive you could look into Paragard, which is a copper IUD, inserted into the uterus it doesn't change hormones, etc. Can be difficult to talk some health providers into getting if you haven't had kids (no real reason you shouldn't get one if you haven't yet had kids..). I "stretched" the truth to get one myself because hormone birth control is SCARY and for good reason.
Non-invasive would be the rhythm method (counting the days of fertility), pull-out method, abstinence. lol Unfortunately only abstinence in this case is really that reliable..