Science is honestly the strategy I understand least, but here's what I'd say:
There's no shame making one science set. It's 10VPs over three cards, which is pretty alright for a mix of age I and age II cards (not so great if you need to use age III cards as well). Each card also gives a chain to something else - mostly blues and reds - which is nice. It limits the amount of science other people can go for, while giving you a respectable score boost. In addition, if people deny you extra science, that often means they'll pass you more other cards you can use, and if they don't, then you often have access to 3 VP science cards in a pinch (possibly 5 VP, if you end up going 2-1-1).
In your position, I think this would have been a good choice, and really it's what you ended up doing, accidentally or not. You get some VPs from science, and put added pressure on the other people going science. The people passing science were on your right, which is not great - it means they were taking the cards before you in two ages.
Two science sets is generally the goal I'll go for, if I'm actually doing a science strategy. This gives 26 VPs, and is generally achievable even if others go for science. You want to really play 2 cards in age I, and 2-3 cards in age II. The School is valuable here, as it chains to two other symbols (and if you didn't need those symbols, you did need the tablet of the School itself!) AND there's only one tablet card in age III. Side note: If fighting Science and you aren't sure, bury the School! To build this much science you want access to all three manufactured goods. As before, this opens you up to building 5 VP extra cards - which is below average but still good even in age III, and people will be much more likely to bury science and pass you other cards you can use.
Be aware, 26 VPs is still less than half the score you're probably gunning for, but is also probably less than half the cards you're playing. Don't expect to win if you scrape 2 science sets at the expense of all else.
When playing Babylon, and/or with expansions, three science sets is viable - but it's still a big risk. Three sets requires 9 card plays and gives 48 VPs, and others are very likely to start denying you the cards you need. I'd suggest only going for three sets if nobody else on the table is doing science. Even if you achieve this, 48VPs is not a winning score, but it is pretty close. In the base game, winning scores are typically around 60 VPs, give or take, so with wonder stages and a little extra, this can be almost your entire gameplan. But with expansions, more card plays mean bigger winning scores... with both expansions, you should be looking for more like 70VPs.