Read data from mysql database for last 24 hours, last week and last month

SELECT info FROM table
WHERE date > UNIX_TIMESTAMP(NOW() - INTERVAL 1 DAY);

or

SELECT info FROM table
WHERE date > UNIX_TIMESTAMP(NOW() - INTERVAL 24 HOUR);

or your way

SELECT info FROM table
WHERE date > (UNIX_TIMESTAMP(NOW()) - 86400); 

Here is 48 hours

SELECT info FROM table
WHERE date > UNIX_TIMESTAMP(NOW() - INTERVAL 2 DAY);

or

SELECT info FROM table
WHERE date > UNIX_TIMESTAMP(NOW() - INTERVAL 48 HOUR);

or your way

SELECT info FROM table
WHERE date > (UNIX_TIMESTAMP(NOW()) - (86400 * 2)); 

Here is 30 days

SELECT info FROM table
WHERE date > UNIX_TIMESTAMP(NOW() - INTERVAL 30 DAY);

or your way

SELECT info FROM table
WHERE date > (UNIX_TIMESTAMP(NOW()) - (86400 * 30)); 

Your last expression WHERE date > (UNIX_TIMESTAMP(NOW()) - 86400) is feasible, but requires you to do the number of seconds difference. My additional suggestions lets MySQL do the date computation.