I think this is a very reasonable question in the abstract: besides the number of symbols there are also a number of annoying redundancies (e.g. $\rightarrow$, $\implies$, $\supset$ all stand for implication). That said, I think it would be more appropriate at math.stackexchange.
But I also think it could be made better (and closer to what you mean to ask). Namely, the wiki list that Nat mentions in their comment above is decent, but it doesn't say anything about the task of passing from knowing the individual meanings to parsing a longer expression (or writing such), and I think this is one of the major sources of difficulty (especially how to intuitively parse expressions involving multiple alternating quantifiers). Offhand I don't actually know a great source on how to read logical notation quickly and easily, it's something I just picked up from classes, but I'm sure there is one somewhere.
Tl;dr, I don't think this question is appropriate for this specific site, but I do think a broader version of it - along the lines of "What is a good source for learning basic logical symbols and how to parse longer logical expressions?" - would be a good fit for MSE.