Philosophy is intrinsically about things where there's no clear, objective and universally acclaimed answer. So it's impossible to avoid opinions, even when coming up with a reading list. Every person is going to recommend a different one. I'll give you mine, specifically for you, but (but I can't pretend it's objective):
First, I'd recommend any good beginner text on symbolic logic, because it's. It's at the nexus of mathematics and philosophy, so it would be a good point of overlap with your prior studies (as well as being arguably the least subjective topic in philosophy, at least if you stick to the standard logics). It will also help you understand the structure of philosophical arguments.
Next, I'd recommend Plato, because he's the most important and central figure in Western philosophy, and nearly everyone who came after him was influenced by him. There's a lot of Plato, but Meno would be a good introduction (it's short, and on the topic of mathematics). Apology and Republic are his most famous and influential works.
Next I'd do Descartes' Meditations. They are short, easy to read, and hugely influential. Plus, Descartes was heavily interested in the same questionthing you are--what can we know for sure? In some ways, this work can be seen as a direct answer to your question "How can I overcome my fear of... topics that are not purely factual or logical?" (HeDescartes was also a master mathematician, whose invention of the Cartesian plane revolutionized the field.)
If you start with those, it will give you a good foundation for understanding anything else you might read after that. I won't include many follow-ups because I suspect your philosophical tastes and mine don't coincide, but if you're open to reading something VERY different, I'd recommend Laozi's Dao De Jing.
All of the above should be freely available online in multiple different translations.All of the above should be freely available online in multiple different translations.