Just two quick comments....
First:

open FILEHANDLENAME, ">>storage.txt";
print FILEHANDLENAME $name," ",$num,"$email","\n";
[download]

would probably be better written as:

$datafile = '/full/path/to/storage.txt';  #somewhere near the top
...
open FILEHANDLENAME, ">>$datafile" or die "Couldn't open $datafile for
+ appending: $!";
print FILEHANDLENAME "$name $num $email\n";
[download]

The first line helps us keep certain things configurable, and will probably help us down the line when we want to modify the script slightly. The second line gives us some feedback if our file handle fails (you used this construct later in the script.... its valuable here too) The third line uses interpolation and is much easier to read than the original.

Second:

$line=<FILE>;
while ( my $line = <FILE> ) {
[download]

What is that first line for? Are you purposefully throwing away the first line in the file? It could be that the first line in the datafile is for human consumption (i.e.

---------- BEGIN storage.txt ------------
NAME      EMAIL        PHONE
Joe Blow  joe@joe.com  123-1233
Jon Blow  jon@jon.com  345-3455
---------- END storage.txt ------------
[download]

In that case a comment is warranted, to let everyone else know why that first line is being tossed.

All in all, it looks pretty good.

-Blake