Hello, I’m not sure whether Ninja Forms Basic version supports shortcode, you can try to get help from the author. Replace the build-in contact form with shortcode is very easy. First you need delete all contact form PHP code from Home Page Template, then add shortcode. For example, if you use Contact Form 7 plugin, you need add the following code.
<?php echo do_shortcode('[contact-form-7-example id="1"]'); ?>
Replace the id with the one you created. Also you may need add your own styles for the contact form.