What's the best algorithm to find the shortest path between 2 vertices in a graph?
At least in theory, the most appropriate algorithm is breadth-first search (BFS), which you execute by starting from your source vertex $s$. Once the BFS traversal hits your target vertex $t$, you halt and trace back a chain of predecessors originating from $t$. This procedure runs in linear time, which is optimal.

However, from a practical standpoint, the answer might depend on the topology of your graph. For instance, some other linear time procedure like a bidirectional search can be much more efficient but this is more challenging to determine apriori.