The optimizer chooses the optimal join order as well as the optimal index for each table. The join order can affect which index is the best choice. The optimizer can choose an index as the access path for a table if it is the inner table, but not if it is the outer table (and there are no further qualifications).
The optimizer chooses the join order of tables only in simple FROM clauses. Most joins using the JOIN keyword are flattened into simple joins, so the optimizer chooses their join order.
The optimizer does not choose the join order for outer joins; it uses the order specified in the statement.