A good list of topics and as a bonus a list of free online sources can be found on the American Institute of Mathematics Open Textbook Initiative: https://aimath.org/textbooks/approved-textbooks/
Now as for order, you could start at the first column on the left, then move down and then move on to the second column, etc... It is not a perfect ordering and you can skip and jump around (most likely the very first few you've seen already). But more or less this is a good representation of topics one would encounter in an undergraduate math degree, and for each topic a couple of texts that have been used in such classes and can be used for free online.
As for how to self-learn. It is very similar to learning in class, but requires way more self-motivation (there is no threat of a bad grade). Best is to go section by section, and after each section try to do as much of the exercises as possible. There is really no replacement for doing exercises. Do not worry if you struggle with exercises. If they are too easy, then you are not learning much. As they say: No pain ... no gain.
Many textbooks usually have somewhere in the introduction at least a hint to the lecturer on the best possible course. If you do self study ... you are the "lecturer".
In the end, I would say the difference in textbooks is not that great. There exist terrible textbooks out there to be sure, but any textbook that has been used in a couple of classrooms is most likely good enough for self study. What will make the most difference is how you yourself approach learning, and how much motivation you have. Best might be to fix a schedule for yourself: set aside time for reading, a schedule on how much you want to get through each time, then set aside time for doing exercises for the sections you've read.