#!/usr/bin/env perl
use warnings;
use strict;

my $toFind = 'String';
while (<DATA>) {
    print if /\b$toFind\s/i;
}

__DATA__
this is a string
strings are us
String.c is a file
so string.o is too
I like a good STRING now and again
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This prints:

this is a string
I like a good STRING now and again
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That's possible - but has built-in problems.

for (@list){
    ### This will not match 'String' at the end of the line
    print if /String\s/;
}
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Unless you have a really unusual requirement, the typical thing to do in these cases is to look for the string followed by (or, even more commonly, surrounded by) a boundary or boundaries. Note that these are zero-width assertions - unlike whitespace which actually requires a character:

for (@list){
    print if /String\b/;
}
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This will match your string even if it's at the end of the line.