If you use WooCommerce, and you want your users to be redirected to checkout instead of cart or the product page, then you can do it in a really simple way.

Use this code (taken from http://stackoverflow.com/questions/15592633/woocommerce-add-to-cart-button-redirect-to-checkout):

function redirect_to_checkout() {
    return WC()->cart->get_checkout_url();
}
add_filter ('woocommerce_add_to_cart_redirect', 'redirect_to_checkout');

You can put it in your theme's functions.php file.