The most efficient way to store bit-wise data is to use integer data types. In your case, each check box would represent 1 bit of an integer. For example, if the check boxes were set:
checkbox 1 checked
checkbox 2 unchecked
checkbox 3 checked
this would represent 5 (1*2^2 + 0*2^1 + 1*2^0). Use the following types of integers depending on the number of bits that you need to store:
tiny int: 8 bits
small int: 16 bits
medium int: 24 bits
int: 32 bits
big int: 64 bits
See http://dev.mysql.com/doc/refman/5.6/en/integer-types.html for more info