I started out not thinking much about the issue at all. This is very common, as it is physically unpleasant to think about as well as socially unpleasant in many circumstances. It leads to poll results that are logically at odds with each other, such as considerable support for both "Abortion should be illegal except in the case of rape, incest, or life of the mother," and "Abortion is a matter that should be private between a woman and her doctor." It's not so much that people are stupid - some are, of course - but more that they have queasy feelings about a lot of aspects of the question and are looking for quick escapes in discussion. I did have something of a default to an essay I had read that the issue was largely philosophical: wherever life begins, at that point abortion should be forbidden. It sounded neat and tidy. (It's not.)
Men and women have very similar opinions on the subject. The idea that only women should be deciding is based largely on the bubble that some pro-choice women live in, believing that because all their friends are pro-choice, most women are as well. It ain't so.
When I tagged along with the Jesus people I went very much pro-life, and being an intense sort, immediately went to a strict "life begins at conception" attitude. I have never been far different since then, but I did modify somewhat. At first I wondered if implantation would be a better line to draw. As the information came out that heartbeat and brainwaves in the fetus begin at 5-6 weeks, I leaned toward that. I preferred the point of conception as a line, but felt less inclined to insist on that. But as I became more aware of genetics as the enormous determinant of many human attributes, I drifted back toward conception as the key point. You are you quite hugely at that point.
The question of "when life begins" I eventually discarded. The fetus is living at the time of conception. It's not dead, it's not inanimate. Another question about humanness might rise up, but "life" proved a non-question. When the science was vague, Catholics had a vague standard of "quickening" as the beginning of life. But as we all learned more in the early 19th C, it decided that conception was the true point. I just threw that in for people who have heard that the RCC was not always so strict about life beginning at conception, trying to show that this is a new and perhaps suspect religious idea. That idea is based on some facts, but is not true.
Pre-implantation genetic testing will increasingly be the norm. I had not reconsidered implantation as a dividing line for decades. Perhaps I should bring that one back for examination.
I think it unlikely the SCOTUS will ever overthrow all abortion restrictions entirely. However, some modification of Roe v Wade that returns some authority to the states is quite possible in the next decade, and because even some abortion advocates think it was badly decided, may be overthrown and some new standard erected. Parental notification, clinic regulation according to medical standards, waiting periods, later abortions and especially partial-birth abortions are going to come back into the public debate.