demirel You can run these commands to install composer:
php -r "copy('https://getcomposer.org/installer', 'composer-setup.php');"
php -r "if (hash_file('sha384', 'composer-setup.php') === '48e3236262b34d30969dca3c37281b3b4bbe3221bda826ac6a9a62d6444cdb0dcd0615698a5cbe587c3f0fe57a54d8f5') { echo 'Installer verified'; } else { echo 'Installer corrupt'; unlink('composer-setup.php'); } echo PHP_EOL;"
php composer-setup.php --install-dir=/usr/local/bin --filename=composer
php -r "unlink('composer-setup.php');"
What OS are you using? If I remember correctly, VestaCP only allows using the default built-in PHP version on the OS. If you're using Ubuntu 18.04, you should be fine. Vesta allows configuring SSH access on a per-account basis, so as long as you meet the PHP + MySQL requirements you'll be alright.