Start Linux scripts sequentially with blocking

./script1 && ./script2
The && means "only execute the second part once the first part has completed successful, different to:
./script1; ./script2
Which does the first part, then the second part. Essentially though, without forking or threading (some methods have this inherently), pretty much all programming you do is imperative and does one thing (to the end) at a time. If you need to hold, write a WHILE in your language that loops until (whatever condition) is true.

A sample of how you would do what you want in perl.

#!/usr/bin/perl

use strict; 
use warnings;

# Start the first script
my $first_script = `/script1.sh`;

my $string_to_find = 'Server Blah Blah started';
my $string_not_found = 1;
my $counter = 0; # counter ofcourse start at 0
my $timer = 300; # since your sleep is set for 1 second this will 
                 # count to 300 before exiting

while($string_not_found){
    exit if ($counter > $timer); # this will make the application exit 
                                 # if the give timer is hit
                                 # you can aswell replace it by
                                 # $string_not_found = 0 if...
                                 # if you want it to run the 2nd code
                                 # as an attempt instead of only exiting
    my $last_line = `tail -1 /my/app/log/file.out`;
    if($last_line =~ /$string_to_find/ig) {
        $string_not_found = 0;
    }else {
        # sleep a little
     $counter++;
        sleep 1;
    }
}
# By the time we are here we are good to go with the next script.
my $second_script = `/script2.sh`;
print 'Finished';
exit;

With the above code it will only run the second program if the word was found once the first program finish printing it is output.

UPDATE: If the program does not output what you want but there is a log file where it will write the info you need, you can use it within perl aswell so your not limited at all.

#!/usr/bin/perl

# Start the first script
$first_script = `/script1.sh`;

$string_to_find = 'Server Blah Blah started';
$string_not_found = 1;
while($string_not_found){
    $last_line = `tail -1 /my/app/log/file.out`;
    if($last_line =~ /$string_to_find/ig) {
        $string_not_found = 0;
    }else {
        # sleep a little
        sleep 1;
    }
}
# By the time we are here we are good to go with the next script.
$second_script = `/script2.sh`;
print 'Finished';
exit;

#TODO: Add some sort of counter to abort incase we don't get the string we are searching.