Mysql – Is BIGINT(8) the largest integer MySQL can store

You can use GROUP_CONCAT:

SELECT person_id,
   GROUP_CONCAT(hobbies SEPARATOR ', ')
FROM peoples_hobbies
GROUP BY person_id;

As Ludwig stated in his comment, you can add the DISTINCT operator to avoid duplicates:

SELECT person_id,
   GROUP_CONCAT(DISTINCT hobbies SEPARATOR ', ')
FROM peoples_hobbies
GROUP BY person_id;

As Jan stated in their comment, you can also sort the values before imploding it using ORDER BY:

SELECT person_id, 
       GROUP_CONCAT(hobbies ORDER BY hobbies ASC SEPARATOR ', ')
FROM peoples_hobbies
GROUP BY person_id;

As Dag stated in his comment, there is a 1024 byte limit on the result. To solve this, run this query before your query:

SET group_concat_max_len = 2048;

Of course, you can change 2048 according to your needs. To calculate and assign the value:

SET group_concat_max_len = CAST(
                     (SELECT SUM(LENGTH(hobbies)) + COUNT(*) * LENGTH(', ')
                           FROM peoples_hobbies
                           GROUP BY person_id) AS UNSIGNED);

Timestamps in MySQL are generally used to track changes to records, and are often updated every time the record is changed. If you want to store a specific value you should use a datetime field.

If you meant that you want to decide between using a UNIX timestamp or a native MySQL datetime field, go with the native format. You can do calculations within MySQL that way ("SELECT DATE_ADD(my_datetime, INTERVAL 1 DAY)") and it is simple to change the format of the value to a UNIX timestamp ("SELECT UNIX_TIMESTAMP(my_datetime)") when you query the record if you want to operate on it with PHP.