If Perl is an option, you can try this:
perl -lne 'print $1 if /(regex)/' file
To implement case-insensitive matching, add the i
modifier
perl -lne 'print $1 if /(regex)/i' file
To print everything AFTER the match:
perl -lne 'if ($found){print} else{if (/regex(.*)/){print $1; $found++}}' textfile
To print the match and everything after the match:
perl -lne 'if ($found){print} else{if (/(regex.*)/){print $1; $found++}}' textfile