Should I use the datetime or timestamp data type in MySQL?

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.

In MySQL 5 and above, TIMESTAMP values are converted from the current time zone to UTC for storage, and converted back from UTC to the current time zone for retrieval. (This occurs only for the TIMESTAMP data type, and not for other types such as DATETIME.)

By default, the current time zone for each connection is the server's time. The time zone can be set on a per-connection basis, as described in MySQL Server Time Zone Support.

I always use DATETIME fields for anything other than row metadata (date created or modified).

As mentioned in the MySQL documentation:

The DATETIME type is used when you need values that contain both date and time information. MySQL retrieves and displays DATETIME values in 'YYYY-MM-DD HH:MM:SS' format. The supported range is '1000-01-01 00:00:00' to '9999-12-31 23:59:59'.

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The TIMESTAMP data type has a range of '1970-01-01 00:00:01' UTC to '2038-01-09 03:14:07' UTC. It has varying properties, depending on the MySQL version and the SQL mode the server is running in.

You're quite likely to hit the lower limit on TIMESTAMPs in general use -- e.g. storing birthdate.