An extensive discussion of the origin of "Menge" is given in Earliest Known Uses of Some of the Words of Mathematics (scroll down to "Set and Set Theory"). Cantor's (1895) Beitrage zür Begründung der tranfiniten Mengenlehre is one of the earliest uses.
The symbols $\cap,\cup$ were introduced by Giuseppe Peano in Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann (1888).
In this brief work by Schröder (37 pages) the mathematical logic is developed that forms the introduction of the present book. I found it useful to replace the logical symbols $\times,+,A_1,0,1$ used by Schröder by the symbols $\cap,\cup,-A$, ⚪, ⚫ in order to avoid a possible confusion between symbols from logic and from mathematics (a possible confusion noted by Schröder himself). I also introduced the logical symbols $\lt$ and $\gt$, although not strictly necessary...