My initial approach was:
$current = time(); // save this to column CURRENT_TIME with column type VARCHAR
//retrieve it like this
$retrieved = mysql_query(..
The format used by MySQL doesn't need to match the format used by PHP. Choose the best on either side. Databases have date data types for a reason; in MySQL you can choose from these:
http://dev.mysql.com/doc/refman/5.1/en/date-and-time-types.html
In PHP, you basically have three options:
Good old timestamps are easy to handle and you can use them in your MySQL queries —see FROM_UNIXTIME() and UNIX_TIMESTAMP()— but they have serious range issues (you can't rely on them for pre-1970 dates, so they are unsuitable for birthdays).
DateTime objects are powerful and builtin, have no range issues and support time zones. However, they are sometimes not very comfortable to use since they seem to lack some important methods.
You can use a custom date object (third-party or your own DateTime based).