The optimization process and recommendations:

1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
2. Avoid Using Date Functions In Conditions (query line: 7): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. An alternative way is to use a range condition instead of a function call.
3. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
4. Index Function Calls Using Generated Columns (modified query below): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index to optimize the search. Creating and indexing a generated column (supported in MySQL 5.7) will allow MySQL to optimize the search.
5. Use Numeric Column Types For Numeric Values (modified query below): When the database is required to cast values, an index can't be used to enhance performance. It's recommended not to compare numeric columns to quoted values, as the quotes will result in a cast that will prevent index usage.
6. Use Numeric Column Types For Numeric Values (query line: 8): Referencing a numeric value (e.g. 1234) as a string in a WHERE clause might result in poor performance. Possible impacts of storing numbers as varchars: more space will be used, you won't be able to perform arithmetic operations, the data won't be self-validated, aggregation functions like SUM won't work, the output may sort incorrectly and more. If the column is numeric, remove the quotes from the constant value, to make sure a numeric comparison is done.

Optimal indexes for this query:

ALTER TABLE `logs` ADD INDEX `logs_idx_month_date_user_datecreate` (`month_datecreated`,`user`,`dateCreated`);

The optimized query:

SELECT
        * 
    FROM
        logs 
    WHERE
        logs.month_datecreated = 9 
        AND logs.dateCreated BETWEEN '2016-01-01 00:00:00' AND '2016-12-31 23:59:59' 
        AND logs.user = '1234'