BuddyPress.org

You could try using the WordPress API, there is a function called login_redirect()

/**
 * Redirect user after successful login.
 *
 * @param string $redirect_to URL to redirect to.
 * @param string $request URL the user is coming from.
 * @param object $user Logged user's data.
 * @return string
 */
function my_login_redirect( $redirect_to, $request, $user ) {
	//is there a user to check?
	if ( isset( $user->roles ) && is_array( $user->roles ) ) {
		//check for admins
		if ( in_array( 'administrator', $user->roles ) ) {
			// redirect them to the default place
			return $redirect_to;
		} else {
			return home_url();
		}
	} else {
		return $redirect_to;
	}
}

add_filter( 'login_redirect', 'my_login_redirect', 10, 3 );

You need to add something like the code above your child theme functions.php file, or you can create a plugin and add this code to it.

https://codex.wordpress.org/Plugin_API/Filter_Reference/login_redirect

You can achieve this with a custom login link which is accessed by a user on your site front…

<?php echo wp_login_url(home_url('/')); ?>

When clicked the login form will process a redirect after logging in.

That wont work if you access the wp-login.php directly.

@coffeewebdev looks like he’s given you a more all-round solution.