## Edit ##

Note: you can use the same technique for a *custom page template*, with a custom loop via `new WP_Query()`:

    // Post Formats
    $post_formats_array = array(
        post-format-aside,
        post-format-audio,
        post-format-chat,
        post-format-gallery,
        post-format-image,
        post-format-link,
        post-format-status,
        post-format-quote,
        post-format-video
    );
    // Custom query args
    $standard_posts_query_args = array(    
        'tax_query' => array(
            array(
                'taxonomy' => 'post_format',
                'field' => 'slug',
                // Use array defined above,
                // or try omitting 'terms' entirely
                'terms' => $post_formats_array,    			
                'operator' => 'NOT IN'
            )
        )
    );
    // Custom query
    $standard_posts = new WP_Query( $standard_posts_query_args );

    // Custom query loop
    if ( $standard_posts->have_posts() ) : while ( $standard_posts->have_posts() ) : $standard_posts->the_post();
        // Loop markup here
    endwhile; endif;

## Pagination ##

For pagination, [please refer to this Question/Answer][1].


## Original Answer ##

Why not just exclude posts with post formats from the main posts archive?

    function wpse129372_filter_posts_archive( $query ) {
        if ( $query->is_main_query && $query->is_archive() ) {
            $post_formats_array = array(
                post-format-aside,
                post-format-audio,
                post-format-chat,
                post-format-gallery,
                post-format-image,
                post-format-link,
                post-format-status,
                post-format-quote,
                post-format-video
            );
            $tax_query = array(
                array(
                    'taxonomy' => 'post_format',
                    'field' => 'slug',
                    // Use array defined above,
                    // or try omitting 'terms' entirely
                    'terms' => $post_formats_array,    			
                    'operator' => 'NOT IN'
                )
            );
            $query->set( 'tax_query', $tax_query );
        }
    }
    add_action( 'pre_get_posts', 'wpse129372_filter_posts_archive' );

This, paired with (I assume) custom template files (or custom page templates) for posts with post formats, would be a fairly simple way to show only "standard" posts in the archive index.


  [1]: http://wordpress.stackexchange.com/questions/120407/how-to-fix-pagination-for-custom-loops