Users Role and Access

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What you need first is to understand User Roles in WordPress.

Then a plugin to manage custom user roles, like User Role Editor or Members.

In the administrative menu Settings > General, set the default role when a user registers to your custom role:
settings general default user role

The plugin Members has more advanced features, but case you were to use URE some extra functions would be necessary to block any access to the site backend. Here wrapped as a plugin, see comments for details.

<?php
/**
 * Plugin Name: Block Admin Access for Certain Roles
 * Version: 0.2
 * Author: brasofilo 
 * Plugin URI: https://wordpress.stackexchange.com/q/57206/12615
 */

/**
 * When a registered user tries to visit a page for which he doesn't have access,
 * i.e.: http:/example.com/wp-admin/plugins.php,
 * WordPress displays a standard WP error message.
 * This will redirect instead of displaying the message:
 * "You do not have sufficient permissions to access this page."
 */
add_action( 'admin_page_access_denied', 'access_denied_wpse_57206' );
function access_denied_wpse_57206()
{
    wp_redirect(home_url());
    exit();
}

/**
 * Redirect users without 'edit_posts' capability if they try to access using an URL
 * of an admin page that they would have capability to do
 * i.e.: http:/example.com/wp-admin/profile.php
 */
add_action( 'admin_init', 'admin_init_wpse_57206' );
function admin_init_wpse_57206()
{
    if( current_user_can( 'edit_posts' ) ) 
        return;

    wp_redirect( home_url() );
    exit();
}

/**
 * Redirect users with 'pending' and 'subscriber' roles to the home url
 */
add_filter( 'login_redirect', 'login_redirect_wpse_57206' );
function login_redirect_wpse_57206( $url )
{
    global $user;
    if ( isset( $user->roles ) )
    {
        $result = array_intersect( $user->roles, array( 'author', 'subscriber' ) );
        if( !empty( $result ) )
            $url = home_url();
    }
    return $url;
}

/**
 * Hide the admin bar for users without 'edit_posts' capability
 */
add_filter( 'show_admin_bar', 'hide_admin_bar_wpse_51831' );
function hide_admin_bar_wpse_51831( $bool )
{
    if( !current_user_can( 'edit_posts' ) )
        $bool = false;

    return $bool;
}

References: